Class 10: Maths Chapter 4 solutions. Complete Class 10 Maths Chapter 4 Notes.

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## RS Aggarwal Solutions for Class 10 Maths Chapter 4–Quadratic Equations

RS Aggarwal 10th Maths Chapter 4, Class 10 Maths Chapter 4 solutions

**Exercise 10A** Solutions

**Question 1:**

(i) x^{2}-x+3=0 is a quadratic polynomial.

∴ x^{2}-x+3=0 is a quadratic equation.

(ii) 2x^{2}+ 52x-√3=0

⇒ 4x^{2}+5x-2√3=0

Clearly is 4x^{2}+5x-2√3=0 a quadratic polynomial.

∴ 2x^{2}+ 52x-√3=0 is a quadratic equation.

(iii) √2x^{2}+7x+5√2=0 is a quadratic polynomial.

∴ √2x^{2}+7x+5√2=0 is a quadratic equation.

(iv)13x^{2}+15x-2=0

⇒ 5x^{2}+3x-2=0

Clearly, 5x^{2}+3x-2=0 is a quadratic equation.

13x^{2}+15 is a quadratic equation.

(v) x^{2}-3x-√x+4=0 is not a quadratic polynomial since it contains √x, in which power 1/2 of x is not an integer.

∴ x^{2}-3x-√x+4=0 is not a quadratic equation.

(vi) x-6x=3

⇒ x^{2}-3x-6 =0

And (x^{2}-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.

Hence, x-6x=3 is a quadratic equation.

(vii) x+2x= x^{2}

⇒ x^{3}-x^{2}-2 =0

And (x^{3}-x^{2}-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.

Hence, x+2x= x^{2} is not a quadratic equation.

(viii) x2−1×2=5 ⇒ x^{4} -1=5x^{2}

⇒x^{4}-5x^{2}-1 =0

And (x^{4}-5x^{2}-1 =0) being a polynomial of degree 4.

Hence x2−1×2=5 is not a quadratic equation.

**Question 2:**

The given equation is 3x^{2}+2x-1=0

(i) On substituting x = -1 in the equation, we get

(ii) On substituting x=13 in the equation, we get

(iii) On substituting x=−12 in the equation , we get

**Question 3:**

Since x = 1 is a solution of x^{2}+kx+3=0 it must satisfy the equation.

Hence the required value of k = -4**Question 4:**

Since x=34 is a root of ax^{2}+bx-6=0, we have

Again x = -2 being a root of ax^{2}+bx-6=0, we have

Multiplying (2) by 4 adding the result from (1), we get

11a = 44 ⇒ a = 4

Putting a = 4 in (1), we get

**Question 5:**

**Question 6:**

**Question 7:**

Hence, 9 and -9 are the roots of the equation 3x^{2}-243=0.**Question 8:**

Hence, -5 and -7 are the roots of x^{2}+12x+35=0.**Question 9:**

Hence, 11 and 7 are the roots of equation x^{2}=18x-77**Question 10:**

Hence, x=−13 is the repeated root of the equation 9x^{2}+6x+1=0**Question 11:**

Hence, is the repeated root of the equation**Question 12:**

Hence, x=−32, x=−12are the roots of 6x^{2}+11x+3=0**Question 13:**

Hence, x=43 and x=−32 are the roots of equation 6x^{2}+x-12=0

**Question 14:**

Hence, x=−13 and 1 are the roots of the equation 3x^{2}-2x-1=0.**Question 15:**

Hence, x=23 and x=−12are the roots of equation 6x^{2}-x-2=0.**Question 16:**

Hence, x=−116 and x=23 are the roots of 48x^{2}-13x-1=0.**Question 17:**

Hence, x=−53 and x=-2 are the roots of the equation 3x^{2}+11x+10=0**Question 18:**

Hence,x=254 and x=-4 are the roots of the equation 4x^{2}-9x=100.**Question 19:**

Hence, x=49 and 2 are the roots of the equation 9x^{2}-22+8=0**Question 20:**

Hence, x=75 and x=−43 are the roots of the given equation 15x^{2}-28=x.**Question 21:**

Hence, x=13 and -4 are the roots of given equation .**Question 22:**

Hence, 1 and √2 are the roots of the given equation**Question 23:**

**Question 24:**

**Question 25:**

Hence, −7√3 and 7√7 are the roots of given equation.**Question 26:**

Hence, -√7 and 137√7 are the roots of given equation.**Question 27:**

Hence, 26√3 and −6√8are the roots of given equation.**Question 28:**

Hence, 5 and −75are the roots of given equation**Question 29:**

Hence, −15 and 12are the roots of given equation.**Question 30:**

Hence, 2 and 12 are the roots of given equation.**Question 31:**

Hence, −ba and cb are the roots of given equation.**Question 32:**

Hence, −1a2 and 1b2are the roots of given equation.**Question 33:**

Hence, 3a4b and −2b3a are the roots of given equation.**Question 34:**

Hence, a22 and b22are the roots of given equation.**Question 35:**

Hence, 2 and 1 are the roots of the given equation**Question 36:**

Hence, -9 and 7 are the roots of the given equation**Question 37:**

Hence, -4 and 94 are the roots of the given equation**Question 38:**

Hence 4013 and 6 are the roots of the given equation**Question 39:**

Hence, 4 and −29 are the roots of the given equation**Question 40:**

Hence, 3 and 43 are the roots of the given equation.**Question 41:**

Hence, 5 and 12 are the roots of the given equation.**Question 42:**

Putting

the given equation become

Case I:

Case II:

Hence, −32 and -2 are the roots of the given equation**Question 43:**

Putting

the given equation become

Case I:

Case II:

Hence, -1 and −235 are the roots of the given equation**Question 44:**

On putting

the given equation become

Case I:

Case II:

Hence, -10 and −15 are the roots of the given equation.**Question 45:**

Putting

the given equation become

Case I:

Case II:

Hence, -1 and 18 are the roots of the given equation**Question 46:**

The given equation

Hence, (a+b) and (a+b)2 is the roots of the given equation**Question 47:**

Hence, a+bab and 2a+b are the roots of the given equation**Question 48:**

Hence, -2,0 are the roots of the given equation**Question 49:**

Hence, 12 and 12 are the roots of the given equation**Question 50:**

Hence, 3 and 2 are the roots of the given equation.

## RS Aggarwal Solutions for Class 10 Maths Chapter 4: **Download PDF**

RS Aggarwal Solutions for Class 10 Maths Chapter 4–Quadratic Equations

**Download PDF**: RS Aggarwal Solutions for Class 10 Maths Chapter 4–Quadratic Equations PDF

**Chapterwise RS Aggarwal Solutions for Class 10 Maths :**

- Chapter 1–Real Numbers
- Chapter 2–Polynomials
- Chapter 3–Linear Equations In Two Variables
- Chapter 4–Quadratic Equations
- Chapter 5–Arithmetic Progression
- Chapter 6–Coordinate Geometry
- Chapter 7–Triangles
- Chapter 8–Circles
- Chapter 9–Constructions
- Chapter 10–Trigonometric Ratios
- Chapter 11–T Ratios Of Some Particular Angles
- Chapter 12–Trigonometric Ratios Of Some Complementary Angles
- Chapter 13–Trigonometric Identities
- Chapter 14–Height and Distance
- Chapter 15–Perimeter and Areas of Plane Figures
- Chapter 16–Areas of Circle, Sector and Segment
- Chapter 17–Volume and Surface Areas of Solids
- Chapter 18–Mean, Median, Mode of Grouped Data
- Chapter 19–Probability

## About RS Aggarwal Class 10 Book

Investing in an R.S. Aggarwal book will never be of waste since you can use the book to prepare for various competitive exams as well. RS Aggarwal is one of the most prominent books with an endless number of problems. R.S. Aggarwal’s book very neatly explains every derivation, formula, and question in a very consolidated manner. It has tonnes of examples, practice questions, and solutions even for the NCERT questions.

He was born on January 2, 1946 in a village of Delhi. He graduated from Kirori Mal College, University of Delhi. After completing his M.Sc. in Mathematics in 1969, he joined N.A.S. College, Meerut, as a lecturer. In 1976, he was awarded a fellowship for 3 years and joined the University of Delhi for his Ph.D. Thereafter, he was promoted as a reader in N.A.S. College, Meerut. In 1999, he joined M.M.H. College, Ghaziabad, as a reader and took voluntary retirement in 2003. He has authored more than 75 titles ranging from Nursery to M. Sc. He has also written books for competitive examinations right from the clerical grade to the I.A.S. level.

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