MCQ Questions | Class 10 Maths Chapter 4 | Quadratic Equations with Answers

MCQ | Quadratic Equations Class 10 | Sat C

Check the below NCERT MCQ Questions for Class 10 Maths Chapter 4 Quadratic Equations with Answers Pdf free download. MCQ Questions for Class 10 Maths with Answers were prepared based on the latest exam pattern. We have Provided Quadratic Equations Class 10 Maths MCQs Questions with Answers to help students understand the concept very well.

Objective Question | NCERT Maths Class 10

NCERT Solutions Class 10 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	10th
Subject:	Maths
Chapter:	4
Chapters Name:	Quadratic Equations
Medium:	English

Ncert Solutions for Class 10 Maths | Objective Type Questions

You can refer to NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Quadratic Equations | Class 10 Maths | NCERT Solutions

Q1.	Which of the following is not a quadratic equation?
	A. 2(x – 1)² = 4x² – 2x + 1
	B. 2x – x² = x² + 5
	C. (√2x + √3 )² + x² = 3x² – 5x
	D. (x² + 2x)² = x⁴ + 3 + 4x³

Ans: (√2x + √3 )² + x² = 3x² – 5x

Explaination:

2x² + 3 + 2√6 x + x² = 3x² – 5x
2√6x + 5x + 3 = 0

Q2.	If -5 is a root of the quadratic equation 2x² + px – 15 = 0, then
	A. p = 3
	B. p = 5
	C. p = 7
	D. p = 1

Ans: p = 7

Q3.	The equation x² – px + q = 0 p, q ε R has no real roots if :
	A. p² > 4q
	B. p² < 4q
	C. p² = 4q
	D. None of these

Ans: p² < 4q

Q4.	One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are
	A. 7 years, 49 years
	B. 5 years, 25 years
	C. 1 years, 50 years
	D. 6 years, 49 years

Ans: 7 years, 49 years

Q5.	If (x – a) is one of the factors of the polynomial ax² + bx + c, then one of the roots of ax² + bx + c = 0 is
	A. 1
	B. c
	C. a
	D. none of these

Ans: a

Q6.	If (x – a) is one of the factors of the polynomial ax² + bx + c, then one of the roots of ax² + bx + c = 0 is
	A. 1
	B. c
	C. a
	D. none of these

Ans: a

Explaination:

∵ x – a is one of the factors one root = a.

Q7.	Which of the following are the roots of the quadratic equation, x² – 9x + 20 = 0 by factorisation?
	A. 3, 4
	B. 4, 5
	C. 5, 6
	D. 6, 1

Ans: 4, 5

Explaination:

Given equation is x² – 9x + 20 = 0
⇒ x² – 5x – 4x + 20 = 0
⇒ x(x – 5) – 4(x – 5) = 0
⇒ (x – 5) (x – 4) = 0
⇒ either x – 5 = 0 and x – 4 = 0
⇒ x = 5 and x = 4
∴ x = 4 and 5 are the roots/solution of the given quadratic equation.

Q8.	If (1 – p) is a root of the equation x² + px + 1 -p = 0, then roots are
	A. 0, 1
	B. -1, 1
	C. 0, -1
	D. – 1, 2

Ans: 0, -1

Explaination:

(1 -p) is a root
∴ (1 – p)² + p(1 – p)+ 1 – p = 0
⇒ (1 – p)[1 – p + p + 1] = 0
⇒ (1 – p)(2) = 0
⇒ p=1
x²+x = 0
One root = 0 and another root = – 1
∴ roots are 0 and – 1.

Q9.	If a, P are roots of the equation x² + 5x + 5 = 0, then equation whose roots are a + 1 and p + 1 is
	A. x² + 5x – 5 = 0
	B. x² + 3x + 5 = 0
	C. x² + 3x + 1 = 0
	D. none of these

Ans: x² + 3x + 1 =

Explaination:

α + β = -5, αβ = 5.
Required equation is x² – (α + 1 + β + 1)x + (α + 1) (β + 1) = 0
⇒ x² – (α + β + 2)x + (αβ + α + β +1) = 0
⇒ x² – (-5 + 2)x + (5 – 5 + 1) = 0
⇒ x² + 3x + 1 = 0

Q10.	Which of the following equations has two distinct real roots?
	A. 2x² – 3√2x + \(\frac{9}{4}\) =0
	B. x² + x – 5 = 0
	C. x² + 3x + 2√2 = 0
	D. 5x² – 3x + 1 = 0

Ans: x² + x – 5 =
Explaination: (2) D > 0

Q11.	Which of the following equations has no real roots ?
	A. x² – 4x + 3√2 =0
	B. x² + 4x – 3√2 = 0
	C. x² – 4x – 3√2 = 0
	D. 3x² + 4√3x + 4 = 0

Ans: x² – 4x + 3√2 =
Explaination: (1) D < 0

Q12.	(x² + 1)² – x² = 0 has
	A. four real roots
	B. two real roots
	C. no real roots
	D. one real root

Ans: no real roots
Explaination: (3) no real roots

Q13.	If the difference of the roots of the equation x² – bx + c = 0 be 1, then
	A. b² – 4c + 1 = 0
	B. b² + 4c = 0
	C. b² – 4c – 1 – 0
	D. b² – 4c = 0

Ans: b² – 4c – 1 –

Explaination:

Let roots are α and β
⇒ α – β = 1
∵ (α – β)² = (α + β)² – 4αβ
⇒ 1 = b² – 4c
⇒ b² – 4c – 1 = 0

Q14.	If α + β = 4 and α³ + β³ = 44, then a, p are the roots of the equation
	A. 2x² – 7x – 7 = 0
	B. 3x² + 8x + 12 = 0
	C. 3x² – 12x + 5 = 0
	D. none of these

Ans: none of these

Explaination:

α³ + β³ = (α + β)³ – 3αβ(α + β)
⇒ 44 = (4)³ – 3αβ × 4
⇒ 44 – 64 = – 12 αβ
⇒ αβ \(=\frac{20}{12}=\frac{5}{3}\)
∴ quadratic equation is
x² – (α + β)x + αβ = 0
⇒ x² – 4x + \(\frac{5}{3}\) = 0
⇒ 3x² – 12x + 5 = 0

Q15.	If the roots of equation 3x² + 2x + (p + 2)(p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
	A. 0
	B. – 1
	C. \(\frac{1}{2}\)
	D. – 3

Ans: – 3

Explaination:

∵ roots are of opposite sign
∴ product of the roots is negative
⇒ (p + 2)(p – 1) should be negative.
Clearly when p = – 3, (p + 2) (p – 1) is not negative.

Q16.	The value of k for which the equation x² + 2(k + 1)x + k² = 0 has equal roots is
	A. – 1
	B. –\(\frac{1}{2}\)
	C. 1
	D. none of these

Ans: –\(\frac{1}{2}\)

Explaination:

For equal roots, D = 0
⇒ [2(k+ 1)]² – 4 × k²=0
⇒ 4(k + 1)² – 4k² =0
⇒ 4(k² + 2k + 1) – 4k² = 0
⇒ 8k + 4 = 0
⇒ k = \(\frac{-1}{2}\)

Q17.	If the equation x² – (2 + m)x + (-m² – 4m – 4) = 0 has coincident roots, then
	A. m = 0, m = 1
	B. m = 2, m = 2
	C. m = -2, m = -2
	D. m = 6, m = 1

Ans: m = -2, m = -2

Explaination:

For coincident roots, D = 0
⇒ [-(2 + m)]² – 4 × 1 × (- m² – 4m – 4) = 0
⇒ (2 + m)² + 4(m² + 4m + 4) = 0
⇒ (2 + m)² + 4(m + 2)² = 0
⇒ 5(2 + m)² = 0
⇒ (2 + m)² = 0
⇒ m = -2.

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MCQ Questions | Class 10 Maths Chapter 4 | Quadratic Equations with Answers

MCQ | Quadratic Equations Class 10 | Sat C

Objective Question | NCERT Maths Class 10

Ncert Solutions for Class 10 Maths | Objective Type Questions

Quadratic Equations | Class 10 Maths | NCERT Solutions

CBSE Solutions | Ncert Solutions Maths Class 10

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Ncert Solutions for Class 10 Maths

Ncert Solutions for Class 10 Maths Chapter 1

Ncert Solutions for Class 10 Maths Chapter 2

Ncert Solutions for Class 10 Maths Chapter 3

Ncert Solutions for Class 10 Maths Chapter 4

Ncert Solutions for Class 10 Maths Chapter 5

Ncert Solutions for Class 10 Maths Chapter 6

Ncert Solutions for Class 10 Maths Chapter 7

Ncert Solutions for Class 10 Maths Chapter 8

Ncert Solutions for Class 10 Maths Chapter 9

Ncert Solutions for Class 10 Maths Chapter 10

Ncert Solutions for Class 10 Maths Chapter 11

Ncert Solutions for Class 10 Maths Chapter 12

Ncert Solutions for Class 10 Maths Chapter 13

Ncert Solutions for Class 10 Maths Chapter 14

Ncert Solutions for Class 10 Maths Chapter 15

NCERT SOLUTIONS

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