{"id":624306,"date":"2023-09-01T08:06:18","date_gmt":"2023-09-01T08:06:18","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=624306"},"modified":"2023-09-01T08:06:26","modified_gmt":"2023-09-01T08:06:26","slug":"kc-sinha-exercise-7-4-mathematics-solution-class-10-chapter-7-quadratic-equations","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-7-4-mathematics-solution-class-10-chapter-7-quadratic-equations\/","title":{"rendered":"KC Sinha: Exercise 7.4 – Mathematics Solution Class 10 Chapter 7 Quadratic Equations"},"content":{"rendered":"\n\n\n\n\n

Question 1 A<\/h4>\n\n\n\n

Write the discriminate of each of the following quadratic equation:<\/strong><\/p>\n\n\n\n

x2<\/sup> + 4x + 3 =0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (4)2<\/sup> \u2013 4 (1) (3)
d = 16 \u2013 12
d = 4<\/p>\n\n\n\n

\n\n\n\n

Question 1 B <\/h4>\n\n\n\n

Write the discriminate of each of the following quadratic equation:<\/strong><\/p>\n\n\n\n

4x2<\/sup> + 5x + 7 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (5)2<\/sup> \u2013 4 (4) (7)
d = 25 \u2013 112
d = \u201387<\/p>\n\n\n\n

\n\n\n\n

Question 1 C<\/h4>\n\n\n\n

Write the discriminate of each of the following quadratic equation:<\/strong><\/p>\n\n\n\n

2x2<\/sup> + 4x + 5 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (4)2<\/sup> \u2013 4 (2) (5)
d = 16 \u2013 40
d = \u201324<\/p>\n\n\n\n

\n\n\n\n

Question 1 D<\/h4>\n\n\n\n

Write the discriminate of each of the following quadratic equation:<\/strong><\/p>\n\n\n\n

3x2<\/sup> + 5x + 6 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (5)2<\/sup> \u2013 4 (3) (6)
d = 25 \u2013 72
d = \u201347<\/p>\n\n\n\n

\n\n\n\n

Question 1 E<\/h4>\n\n\n\n

Write the discriminate of each of the following quadratic equation:<\/strong><\/p>\n\n\n\n

\u221a3 x2<\/sup> \u2014 2\u221a2 \u2013 2\u221a3 = 0<\/strong>
Sol :
d = b2<\/sup>\u2013 4ac
d = (\u20132\u221a2)2<\/sup> \u2013 4 (\u221a3) (\u20132\u221a3)
d = 8 + 24
d = 32<\/p>\n\n\n\n

\n\n\n\n

Question 2 A<\/h4>\n\n\n\n

Examine whether the following quadratic equations have real roots or not:<\/strong><\/p>\n\n\n\n

7x2<\/sup> + 8x \u2014 1 = 0<\/strong>
Sol :
TO CHECK REAL ROOTS, \u2018d\u2019 SHOULD BE GREATER THAN 0.
d = b2<\/sup> \u2013 4ac
d = (8)2<\/sup>2 \u2013 4 (7) (\u20131)
d = 64 \u2013 28
d = 92
Yes, roots are real.<\/p>\n\n\n\n

\n\n\n\n

Question 2 B <\/h4>\n\n\n\n

Examine whether the following quadratic equations have real roots or not:<\/strong><\/p>\n\n\n\n

2x2<\/sup> + 3x + 4 = 0<\/strong>
Sol :
TO CHECK REAL ROOTS, \u2018d’ SHOULD BE GREATER THAN 0.
d = b2<\/sup>\u2013 4ac
d = (3)2<\/sup> \u2013 4(2)(4)
d = 9 \u2013 32
d = \u2013 23
No, roots aren\u2019t real.<\/p>\n\n\n\n

\n\n\n\n

Question 2 C<\/h4>\n\n\n\n

Examine whether the following quadratic equations have real roots or not:<\/strong><\/p>\n\n\n\n

x2<\/sup> \u2014 12x \u2014 16 = 0<\/strong>
Sol :
TO CHECK REAL ROOTS, \u2018d’ SHOULD BE GREATER THAN 0.
d = b2<\/sup> \u2013 4ac
d = (\u201312)2<\/sup> \u2013 4 (1) (\u201316)
d = 144 \u2013 64
d = 208
Yes, roots are real .<\/p>\n\n\n\n

\n\n\n\n

Question 2 D<\/h4>\n\n\n\n

Examine whether the following quadratic equations have real roots or not:<\/strong><\/p>\n\n\n\n

x2<\/sup> + x \u2013 1= 0<\/strong>
Sol :
TO CHECK REAL ROOTS, \u2018d’ SHOULD BE GREATER THAN 0.
d = b2<\/sup> \u2013 4ac
d = (1)2<\/sup> \u2013 4 (1) (\u20131)
d = 1 + 4
d = 5
Yes, roots are real.<\/p>\n\n\n\n

\n\n\n\n

Question 2 E<\/h4>\n\n\n\n

Examine whether the following quadratic equations have real roots or not:<\/strong><\/p>\n\n\n\n

x2<\/sup> \u2014 10x + 2 = 0<\/strong>
Sol :
TO CHECK REAL ROOTS, \u2018d’ SHOULD BE GREATER THAN 0.
d = b2<\/sup> \u2013 4ac
d = (\u201310)2<\/sup> \u2013 4 (1) (2)
d = 100 \u2013 8
d = 92
Yes, roots are real.<\/p>\n\n\n\n

\n\n\n\n

Question 3 A<\/h4>\n\n\n\n

Find whether the following quadratic equations have a repeated root :<\/strong><\/p>\n\n\n\n

9x2<\/sup>\u2014 12x + 4 = 0<\/strong>
Sol :
REPEATED ROOTS MEAN d = 0.
d = b2<\/sup> \u2013 4ac
d = (\u201312)2<\/sup> \u2013 4(9)(4)
d = 144 \u2013 144
d = 0
Yes, roots are repeated.<\/p>\n\n\n\n

\n\n\n\n

Question 3 B <\/h4>\n\n\n\n

Find whether the following quadratic equations have a repeated root :<\/strong><\/p>\n\n\n\n

y2<\/sup> \u2014 6y + 6 = 0<\/strong>
Sol :
REPEATED ROOTS MEAN d = 0.
d = b2<\/sup> \u2013 4ac
d = (\u20136)2<\/sup> \u2013 4(1)(6)
d = 36 \u2013 24
d = 12
\u2234 roots are not repeated.<\/p>\n\n\n\n

\n\n\n\n

Question 3 C<\/h4>\n\n\n\n

Find whether the following quadratic equations have a repeated root :<\/strong><\/p>\n\n\n\n

9x2<\/sup> + 4x + 6 = 0<\/strong>
Sol :
REPEATED ROOTS MEAN d = 0.
d = b2<\/sup> \u2013 4ac
d = (4)2<\/sup> \u2013 4 (9) (6)
d = 16 \u2013 216
d = \u2013200
\u2234 roots are not repeated.<\/p>\n\n\n\n

\n\n\n\n

Question 3 D<\/h4>\n\n\n\n

Find whether the following quadratic equations have a repeated root :<\/strong><\/p>\n\n\n\n

16y2<\/sup>\u2014 40y + 25 = 0<\/strong>
Sol :
REPEATED ROOTS MEAN d = 0 .
d = b2<\/sup> \u2013 4ac
d = (\u201340)2<\/sup> \u2013 4 (16) (25)
d = 1600 \u2013 1600
d = 0
\u2234 roots are repeated.<\/p>\n\n\n\n

\n\n\n\n

Question 3 E<\/h4>\n\n\n\n

Find whether the following quadratic equations have a repeated root :<\/strong><\/p>\n\n\n\n

x2<\/sup> + 6x + 9 = 0<\/strong>
Sol :<\/p>\n\n\n\n

REPEATED ROOTS MEAN d = 0 .
d = b2<\/sup> \u2013 4ac
d = (6)2<\/sup> \u2013 4(1)(9)
d = 36 \u2013 36
d = 0
\u2234 roots are repeated.<\/p>\n\n\n\n

\n\n\n\n

Question 4 A<\/h4>\n\n\n\n

Comment upon the nature of roots of the following equations:<\/strong><\/p>\n\n\n\n

4x2<\/sup> + 7x + 2 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (7)2<\/sup> \u2013 4 (4) (2)
d = 49 \u2013 32
d = 17
Since, d>0, roots are unique and real.<\/p>\n\n\n\n

\n\n\n\n

Question 4 B <\/h4>\n\n\n\n

Comment upon the nature of roots of the following equations:<\/strong><\/p>\n\n\n\n

x2<\/sup> + 10x + 39 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (10)2<\/sup> \u2013 4 (1) (39)
d = 100 \u2013 156
d = \u201356
Since, d < 0, no real roots exists.<\/p>\n\n\n\n

\n\n\n\n

Question 5 A<\/h4>\n\n\n\n

Without solving, determine whether the following equations have real roots or not. If yes, find them:<\/strong><\/p>\n\n\n\n

2x2<\/sup>\u2014 4x + 3 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (\u20134)2<\/sup> \u2013 4 (2) (3)
d = 16 \u2013 24
d = \u20138
Since, d < 0, no real roots exist for the given equation.<\/p>\n\n\n\n

\n\n\n\n

Question 5 B<\/h4>\n\n\n\n

Without solving, determine whether the following equations have real roots or not. If yes, find them:<\/strong><\/p>\n\n\n\n

y2\u221223y+19=0<\/p>\n\n\n\n

Sol :
d = b2<\/sup> \u2013 4ac
d=(\u221223)2\u22124(1)(19)
d=49\u221249
d = 0
Since, d = 0, roots are real and equal for the given equation.
x=\u2212b\u00b1d\u221a2a
x=\u2212(\u221223)\u00b10\u221a2\u00d71
x=23\u00d712
x=13<\/p>\n\n\n\n

\n\n\n\n

Question 6 A<\/h4>\n\n\n\n

Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:<\/strong><\/p>\n\n\n\n

2x2<\/sup>\u2014 6x + 3 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (\u20136)2<\/sup> \u2013 4 (2) (3)
d = 36 \u2013 24
d = 12
\u2234 Roots are real and unique.<\/p>\n\n\n\n

\n\n\n\n

Question 6 B<\/h4>\n\n\n\n

Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:<\/strong><\/p>\n\n\n\n

2x2<\/sup> \u2014 5x \u2014 3 = 0<\/strong>
Sol :
d = b2<\/sup> \u2013 4ac
d = (\u20135)2<\/sup> \u2013 4 (2) (\u20133)
d = 25 + 24
d = 49
\u2234 Roots are real and unique.<\/p>\n\n\n\n

\n\n\n\n

Question 7 A <\/h4>\n\n\n\n

Find the value of k for which the quadratic equation<\/strong><\/p>\n\n\n\n

4x2<\/sup> \u2014 2 (k + 1) x + (k + 4) = 0 has equal roots.<\/strong>
Sol :
Since roots are equal
\u2234 d=0 \u2026.(1)
4x2<\/sup> \u2014 2 (k + 1) x + (k + 4) = 0
d = b2<\/sup> \u2013 4ac
d = (\u20132 (k + 1)2<\/sup> \u2013 4 (4) (k + 4)
d = (\u2013 2k \u2013 2)2<\/sup> \u2013 16k \u2013 64
d = 4k2<\/sup> + 4 + 8k \u2013 16k \u2013 64
(\u2235 (a \u2013 b)2<\/sup> = a2<\/sup> + b2<\/sup> \u2013 2ab)
d = 4k2<\/sup> \u2013 8k \u2013 60
From (1), d = 0
\u2234 Equation will be:
4k2<\/sup> \u2013 8k \u2013 60 = 0
Dividing by 4
k2<\/sup> \u2013 2k \u2013 15 = 0
4k2<\/sup> \u2013 5k + 3k \u2013 15 = 0
k (k \u2013 5) + 3(k \u2013 5) = 0
(k \u2013 5) (k + 3) = 0
K \u2013 5 = 0 k + 3 = 0
K = 5 k = \u20133<\/p>\n\n\n\n

\n\n\n\n

Question 7 B<\/h4>\n\n\n\n

Find the value of k, so that the quadratic equation<\/strong><\/p>\n\n\n\n

(k + 1) x2<\/sup> \u2013 2 (k \u2014 1) x + 1 = 0 has equal roots.<\/strong>
Sol :
Since roots are equal
\u2234 d=0 \u2026.(1)
(k + 1)x2<\/sup> \u2014 2 (k \u2013 1) x + 1 = 0
d = b2<\/sup> \u2013 4ac
d = (\u20132(k\u20131))2<\/sup>\u2013 4(k+1)(1)
d = (\u20132k+2)2<\/sup> \u2013 4k \u2013 4
d=4k2<\/sup> + 4 \u2013 8k \u2013 4k \u2013 4
(\u2235 (a + b)2<\/sup> = a2<\/sup> + b2<\/sup> + 2ab)
d = 4k2<\/sup> \u2013 12k
From (1), d = 0
\u2234 Equation will be:
0 = 4k2<\/sup> \u2013 12k
4k2<\/sup> = 12k
k2=124k
k2<\/sup> = 3k
k2<\/sup> \u2013 3k = 0
k(k \u2013 3) = 0
k = 0 or k \u2013 3 = 0
k = 3
\u2234 Values of k are 0, 3.<\/p>\n\n\n\n

\n\n\n\n

Question 8 A<\/h4>\n\n\n\n

For what values of k, does the following quadratic equation has equal roots.<\/strong><\/p>\n\n\n\n

9x2<\/sup> + 8kx + 16 = 0<\/strong>
Sol :
Since roots are equal
\u2234 d=0 (1)
9x2<\/sup> + 8kx + 16 = 0
d = b2<\/sup> \u2013 4ac
d = (8k)2<\/sup> \u2013 4 (9) (16)
From (1), d = 0
\u2234 Equation will be:
0 = 64k2<\/sup> \u2013 576
k2=57664
k2<\/sup> = 9
k = \u00b1\u221a9
k = 3, \u20133
\u2234 values of k are \u20133, 3 .<\/p>\n\n\n\n

\n\n\n\n

Question 8 B<\/h4>\n\n\n\n

(k + 4)x2<\/sup> + (k + 1)x + 1 = 0<\/strong><\/p>\n\n\n\n

Sol :
Since roots are equal
\u2234 d=0 (1)
(k + 4)x2<\/sup> + (k + 1)x + 1 = 0
d=b2<\/sup>\u20134ac
d = (k \u2013 1)2<\/sup>\u2013 4 (k + 4) (1)
d = (\u20132k + 2)2<\/sup> \u2013 4k \u2013 4
d = k2<\/sup> + 1+ 2k \u2013 4k \u2013 16
From (1), d = 0
\u2234 Equation will be:
0 = k2<\/sup> + 1 + 2k \u2013 4k \u2013 16
k2<\/sup> \u2013 2k \u2013 15 = 0
k2<\/sup> \u2013 5k + 3k \u2013 15 = 0
k(k \u2013 5) + 3 (k \u2013 5) = 0
(k \u2013 5) (k + 3) = 0
K \u2013 5 = 0 k + 3 = 0
k = 5 k = \u20133
\u2234 Values of k are \u20133, 5.<\/p>\n\n\n\n

\n\n\n\n

Question 8 C<\/h4>\n\n\n\n

k2<\/sup>x2<\/sup> \u2014 2(2k \u2014 1)x + 4 = 0<\/strong><\/p>\n\n\n\n

Sol :
Since roots are equal
\u2234 d=0 (1)
k2<\/sup>x2<\/sup> \u2014 2(2k \u2014 1)x + 4 = 0
d = b2<\/sup> \u2013 4ac
d = (\u20132(k\u20131))2<\/sup> \u2013 4 (k2<\/sup>) (4)
d = (\u20132k+2)2<\/sup> \u2013 4k \u2013 4
d = (\u20134k+2)2<\/sup> \u2013 16k2<\/sup>
(\u2235 (a \u2013 b)2<\/sup> = a2<\/sup> + b2<\/sup> \u2013 2ab)
d = 16k2<\/sup> \u2013 16k + 4 \u2013 16k2<\/sup>
d = \u201316k + 4
From (1), d = 0
\u2234 Equation will be:
0 = \u201316k + 4
16k = 4


\u2234 Values of k are is .<\/p>\n\n\n\n

\n\n\n\n

Question 9 <\/h4>\n\n\n\n

If the roots of the equation (a \u2014 b)x2<\/sup> + (b \u2014 c) x + (c \u2014 a) = 0 are equal, prove that 2a = b + c.<\/strong><\/p>\n\n\n\n

Sol :
Since roots are equal
\u2234 d=0 (1)
(a \u2014 b)x2<\/sup> + (b \u2014 c) x + (c \u2014 a) = 0
d = b2<\/sup> \u2013 4ac
d = (b\u2013c)2<\/sup> \u2013 4 (a\u2013b) (c\u2013a)
d = b2<\/sup> + c2<\/sup> \u2013 2bc \u20134 [a (c \u2013 a) \u2013 b (c \u2013 a)]
d = b2<\/sup> + c2<\/sup> \u2013 2bc \u2013 4 [ac \u2013 a2<\/sup> \u2013 bc + ba]
From (1), d = 0
\u2234 Equation will be:
0 = b2<\/sup> + c2<\/sup> \u2013 2bc \u2013 4ac + 4a2<\/sup> + 4bc \u2013 4ba
b2<\/sup> + c2<\/sup> \u2013 (2a)2<\/sup> 2bc + 2c (\u20132a) + 2(\u20132a)b = 0
(b + c \u2013 2a)2<\/sup> = 0
(b + c \u2013 2a) = 0
b + c = 2a
Hence proved.<\/p>\n\n\n\n

\n\n\n\n

Question 10<\/h4>\n\n\n\n

If \u2014 5 is a root of the quadratic equation 2x2<\/sup> + 2px \u2014 15 = 0 and the quadratic equation p (x2<\/sup> + x) + k = 0 has equal roots, find the value of k.<\/strong><\/p>\n\n\n\n

Sol :
2x2<\/sup> + 2px \u2014 15 = 0
Put x = \u20135
2(\u20135)2<\/sup> + 2p(\u20135) \u2014 15 = 0
50 \u2013 10p \u2013 15 = 0
35 = 10p
p = 3.5
Equation p (x2<\/sup> + x) + k = 0 has equal roots i.e. d = 0
p (x2<\/sup> + x) + k = 0
p = 3.5
3.5 (x2<\/sup> + x) + k = 0
3.5x2<\/sup> + 3.5x + k = 0
d = b2<\/sup> \u2013 4ac
d = (3.5)2<\/sup> \u2013 4(3.5)(k)
d = 12.25 \u2013 14k
Putting d = 0
\u2234 Equation will be:
0 = 12.25 \u2013 14k
14k = 12.25
k=12.2514
k = 0.875<\/p>\n\n\n\n

\n\n\n\n

Question 11 A<\/h4>\n\n\n\n

Find the values of k, for which the given equation has real roots:<\/strong><\/p>\n\n\n\n

2x2<\/sup> \u2014 10x + k = 0<\/strong><\/p>\n\n\n\n

Sol :
Roots are equal
\u2234 d = 0
d = b2<\/sup> \u2013 4ac
d = (\u201310)2<\/sup> \u2013 4 (2) (k)
d = 100 \u2013 8k
Put d = 0
0 = 100 \u2013 8k
8k = 100<\/p>\n\n\n\n

k=1008<\/p>\n\n\n\n

k=252<\/p>\n\n\n\n

\n\n\n\n

Question 11 B<\/h4>\n\n\n\n

Find the values of k, for which the given equation has real roots:<\/strong><\/p>\n\n\n\n

kx2<\/sup> \u2014 6x \u2014 2 = 0<\/strong>
Sol :
Roots are equal
\u2234 d = 0
d = b2<\/sup> \u2013 4ac
d = (\u20136)2<\/sup> \u2013 4 (\u20132) (k)
d = 36 + 8k
Put d = 0
0 = 36 + 8k
\u20138k = 36<\/p>\n\n\n\n

k=\u2212368<\/p>\n\n\n\n

k=\u221292<\/p>\n\n\n\n

\n\n\n\n

Question 11 C<\/h4>\n\n\n\n

Find the values of k, for which the given equation has real roots:<\/strong><\/p>\n\n\n\n

kx2<\/sup>+ 4x + 1 = 0<\/strong>
Sol :
Roots are equal
\u2234 d = 0
d = b2<\/sup> \u2013 4ac
d = (4)2<\/sup> \u2013 4 (1) (k)
d = 16 \u2013 4k
Put d = 0
0 = 16 \u2013 4k
4k = 16
k = 4<\/p>\n\n\n\n

\n\n\n\n

Question 11 D<\/h4>\n\n\n\n

Find the values of k, for which the given equation has real roots:<\/strong><\/p>\n\n\n\n

kx2<\/sup> \u2013 2\u221a5x + 4 = 0<\/strong>
Sol :
Roots are equal
\u2234 d = 0
d = b2<\/sup> \u2013 4ac
d = (\u20132\u221a5)2<\/sup> \u2013 4 (k) (4)
d = 20 \u2013 16k
Put d = 0
0 = 20 \u2013 16k
16k = 20<\/p>\n\n\n\n

k=2016<\/p>\n\n\n\n

k=54<\/p>\n\n\n\n

\n\n\n\n

Question 11 E<\/h4>\n\n\n\n

Find the values of k, for which the given equation has real roots:<\/strong><\/p>\n\n\n\n

x2<\/sup> + k(4x + k \u2014 1) + 2 = 0<\/strong>
Sol :
Roots are equal
\u2234 d = 0
d = b2<\/sup> \u2013 4ac
d = (4k)2<\/sup> \u2013 4 (k2<\/sup> \u2013 k + 2) (1)
d = 16k2<\/sup> \u2013 4k2<\/sup> + 4k \u2013 8
Put d = 0
0 = 16k2<\/sup> \u2013 4k2<\/sup> + 4k \u2013 8
12k2<\/sup> + 4k2<\/sup> + 4k \u2013 8 = 0 (divide by 4)
3k2<\/sup> + k \u2013 2 = 0
3k2<\/sup> + 3k \u2013 2k \u2013 2 = 0
3k (k + 1) \u2013 2k (k + 1) = 0
(3k\u20132k)(k+1) = 0
(3k\u20132k)=0 or (k+1) = 0
k = 0 k = \u20131<\/p>\n\n\n\n

\n\n\n\n

Question 12<\/h4>\n\n\n\n

Prove that the equation x2<\/sup>(a2<\/sup> + b2<\/sup>) + 2x(ac + bd) + (c2<\/sup> + d2<\/sup>)= 0 has no real root, if ad \u2260 bc.<\/strong><\/p>\n\n\n\n

Sol :
x2<\/sup>(a2<\/sup> + b2<\/sup>) + 2x(ac + bd) + (c2<\/sup> + d2<\/sup>)= 0
d = b2<\/sup> \u2013 4ac
d = (2ac + 2bd)2<\/sup> \u2013 4 (a2<\/sup> + b2<\/sup>) (c2<\/sup> + d2<\/sup>)
d = 4a2<\/sup>c2<\/sup> + 4b2<\/sup>d2<\/sup> + 8abcd \u2013 4 [a2<\/sup> (c2<\/sup> + d2<\/sup>) + b2<\/sup> (c2<\/sup>+d2<\/sup>)]
d = 4a2<\/sup>c2<\/sup> + 4b2<\/sup>d2<\/sup> + 8abcd \u2013 4 [a2<\/sup>c2<\/sup> + a2<\/sup>d2<\/sup> + b2<\/sup>c2<\/sup> + b2<\/sup>d2<\/sup>]<\/p>\n\n\n\n

d = 4a2<\/sup>c2<\/sup> + 4b2<\/sup>d2<\/sup> + 8abcd \u2013 4a2<\/sup>c2<\/sup> \u2013 4a2<\/sup>d2<\/sup> \u2013 4b2<\/sup>c2<\/sup> \u2013 4b2<\/sup> d2<\/sup>
d = 8abcd \u2013 4a2<\/sup>d2<\/sup> \u2013 4b2<\/sup>c2<\/sup>
d = 8abcd \u2013 4(a2<\/sup>d2<\/sup> + b2<\/sup> c2<\/sup>)
d = \u20134 (a2<\/sup> d2<\/sup> + b2<\/sup>c2<\/sup> \u2013 2abcd)
d = \u20134 [(ad + bc)2<\/sup>]
For ad \u2260 bc
d= \u20134 \u00d7 [value of (ad + bc)2<\/sup>]
\u2234 d is always negative
So, d < 0
The given equation has no real roots.<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 10 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Question 1 A Write the discriminate of each of the following quadratic equation: x2 + 4x + 3 =0Sol :d = b2 \u2013 4acd = (4)2 \u2013 4 (1) (3)d = 16 \u2013 12d = 4 Question 1 B  Write the discriminate of each of the following quadratic equation: 4×2 + 5x + 7 = 0Sol :d = b2 \u2013 […]<\/p>\n","protected":false},"author":302,"featured_media":624299,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[24],"tags":[],"boards":[],"class_list":["post-624306","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","entry"],"yoast_head":"\nKC Sinha: Exercise 7.4 - Mathematics Solution Class 10 Chapter 7 Quadratic Equations - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"Question 1 A Write the discriminate of each of the following quadratic equation: x2 + 4x + 3 =0Sol :d = b2 \u2013 4acd = (4)2 \u2013 4 (1) (3)d = 16\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-7-4-mathematics-solution-class-10-chapter-7-quadratic-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 7.4 - 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