Please refer to Chapter 4 Quadratic Equation MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Quadratic Equation and then attempt the following objective questions.

MCQ Questions Class 10 Mathematics Chapter 4 Quadratic Equation

The Quadratic Equation MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. What is the relation between speed ,distance and time?     
(a) speed = (distance )/time
(b) distance = (speed )/time
(c) time = speed x distance
(d) speed = distance x time

Question. Find the product of the roots of x² + 8x – 16 = 0
(a) 8
(b) –8
(c) 16
(d) –16

Question. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be   
(a) 20 km/hr
(b) (20 + x) km/hr
(c) (20 – x) km/hr
(d) 2 km/hr

Question. If the equation (1 + m²) x² + (2mc) x + (c² – a²) = 0 has equal roots, then
(a) c² – a² = 1 + m²
(b) c² = a² (1 + m²)
(c) c²a² = (1 + m²)
(d) c² + a² = 1 + m²

Question. Which of the following satisfy the equation a²b²x² + b²x – a²x – 1 = 0
(a) 1/a²
(b) 1/ b²
(c)  −1 / b²
(d) None of these

Question. If the equation x² + 2(k + 2)x + 9k = 0 has equal roots, then k = ?   
(a) 1 or 4
(b) –1 or 4
(c) 1 or – 4
(d) –1 or – 4

Question. If x² + y² = 25, xy = 12, then x =
(a) {3, 4}
(b) {3, –3}
(c) {3, 4, –3, –4}
(d) {–3, –3}

Question. The roots of the quadratic equation x² – 0.04 = 0 are
(a) ± 0.2
(b) ± 0.02
(c) 0.4
(d) 2

Question. How much time boat took in downstream?   
(a) 90 minute
(b) 15 minute
(c) 30 minute
(d) 45 minute

Question. If the product of roots of the equation x3 – 3x + k = 10 is –2, then the value of k is   
(a) –2
(b) –8
(c) 8
(d) 12

Question. One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x² correctly as –6 and 1 respectively. The correct roots are
(a) 3, –2
(b) –3, 2
(c) –6, –1
(d) 6, –1

Question. If the roots of 5x² – kx + 1 = 0 are real and distinct, then   
(a) −2√5 < k < 2√5
(b) k > 2√5 only
(c) k < −2√ 5 only
(d) either k > 2 √5 or k < −2√5

Question. If a – b, b – c are the roots of ax² + bx + c = 0, then find the value of (a b)(b c)/c a   
(a) b/ c
(b) c/ b
(c) ab/ c
(d) bc

Question. If x = √7 + 4√3 , then x +1/x=   
(a) 4
(b) 6
(c) 3
(d) 2

Question. What will be the distance covered by Ajay’s car in two hours?   
(a) 2(x +5)km
(b) (x – 5)km
(c) 2( x + 10)km
(d) (2x + 5)km

Question. If the roots of the equation px² + 2qx + r = 0 and qx2 − 2√ pr x + q = 0 be real, then
(a) p = q
(b) q² = pr
(c) p² = qr
(d) r² = pq

Question. Which of the following is not a quadratic equation?
(a) x² – 2x + 2 (3 – x) = 0
(b) x (x + 1) + 1 = (x – 2) (x – 5)
(c) (2x – 1) (x – 3) = (x + 5) (x – 1)
(d) x³ – 4x² – x + 1 = (x –2)³

Question. The equation 2x² + 2(p + 1) x + p = 0, where p is real, always has roots that are
(a) Equal
(b) Equal in magnitude but opposite in sign
(c) Irrational
(d) Real

Question. If one root of 5x² + 13x + k = 0 be the reciprocal of the other root, then the value of k is   
(a) 0
(b) 1
(c) 2
(d) 5

Question. The condition for one root of the quadratic equation ax² + bx + c = 0 to be twice the other, is
(a) b² = 4ac
(b) 2b² = 9ac
(c) c² = 4a + b²
(d) c² = 9a – b²

Question. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is     
(a) x² – 6x + 6 = 0
(b) x² + 6x – 6 = 0
(c) x² – 6x – 6 = 0
(d) x² + 6x + 6 = 0

Question. If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other, then
(a) b = c
(b) a = b
(c) ac = 1
(d) a = c

Question. What is the speed of current ?   
(a) 20 km/hour
(b) 10 km/hour
(c) 15 km/hour
(d) 25 km/hour

Question. The roots of the equation x +1/x=3.1/3x ≠0,  are
(a) 3, 1
(b) 3, 1/ 3
(c) 3, -1/ 3
(d) – 3, 1/ 3

Question. If (x-1/2)²−(x-3/2)² =x+2 , then x =
(a) 3
(b) 2
(c) 4
(d) None of these

Question. If the equation (m² + n²) x² –2 (mp + nq) x + p² + q² = 0 has equal roots, then
(a) mp = nq
(b) mq = np
(c) mn = pq
(d) mq = √np

Question. If the ratio of the roots of the equation x² + bx + c = 0 is the same as that of x² + qx + r = 0, then
(a) r²b = qc²
(b) r²c = qb²
(c) c²r = q²b
(d) b²r = q²c

Question. If a and b are the roots of the quadratic equation x² – 6x – 2 = 0 and if an = an – bn, then the value of  a₁₀-2a_g / 2a₉  is
(a) 6.0
(b) 5.2
(c) 5.0
(d) 3.0

Fill in the Blanks :

Question. A quadratic equation cannot have more than …….. roots.

Question. If r, s are roots of ax² + bx + c = 0, then is ……….

Question. The equation ax² + bx + c = 0, a ≠ 0 has no real roots, if ………

Question. A quadratic equation ax² + bx + c = 0 has two distinct real roots, if b² – 4ac …………..

Question. The values of k for which the equation 2x² + kx + x + 8 = 0 will have real and equal roots are ………….

Question. If a, b are the roots of x² + x + 1 = 0, then a2 + b2 = ………..

True Or False :

Question. For the expression ax² + 7x + 2 to be quadratic, the possible values of a are non-zero real numbers.

Question. (x – 2) (x + 1) = (x – 1) (x + 3) is a quadratic equation.

Question. The roots of the equation (x – 3)2 = 3 are 3± 3

Question. A quadratic equation cannot be solved by the method of completing the square.

Question. Sum of the reciprocals of the roots of the equation x² + px + q = 0 is 1/p.

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