# Quadratic Equation MCQ Class 10 Mathematics

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

**Answer**

A

**Question. Find the product of the roots of x ^{2} + 8x – 16 = 0 **

(a) 8

(b) –8

(c) 16

(d) –16

**Answer**

D

**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

**Answer**

C

**Question. If the equation (1 + m ^{2}) x^{2} + (2mc) x + (c^{2} – a^{2}) = 0 has equal roots, then **

(a) c

^{2}– a

^{2}= 1 + m

^{2}

(b) c

^{2}= a

^{2}(1 + m

^{2})

(c) c

^{2}a

^{2}= (1 + m

^{2})

(d) c

^{2}+ a

^{2}= 1 + m

^{2}

**Answer**

B

**Question. Which of the following satisfy the equation a ^{2}b^{2}x^{2} + b^{2}x – a^{2}x – 1 = 0 **

(a) 1/a

^{2}

(b) 1/ b

^{2}

(c) −1 / b

^{2}

(d) None of these

**Answer**

B

**Question. If the equation x ^{2} + 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

**Answer**

A

**Question. If x ^{2} + y^{2} = 25, xy = 12, then x = **

(a) {3, 4}

(b) {3, –3}

(c) {3, 4, –3, –4}

(d) {–3, –3}

**Answer**

C

**Question. The roots of the quadratic equation x ^{2} – 0.04 = 0 are **

(a) ± 0.2

(b) ± 0.02

(c) 0.4

(d) 2

**Answer**

A

**Question. How much time boat took in downstream? **

(a) 90 minute

(b) 15 minute

(c) 30 minute

(d) 45 minute

**Answer**

C

**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

**Answer**

C

**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 x ^{2} correctly as –6 and 1 respectively. The correct roots are **

(a) 3, –2

(b) –3, 2

(c) –6, –1

(d) 6, –1

**Answer**

D

**Question. If the roots of 5x ^{2} – 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

**Answer**

D

**Question. If a – b, b – c are the roots of ax ^{2} + 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

**Answer**

B

**Question. If x = √7 + 4√3 , then x +1/x= **

(a) 4

(b) 6

(c) 3

(d) 2

**Answer**

A

**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

**Answer**

A

**Question. If the roots of the equation px ^{2} + 2qx + r = 0 and qx2 − 2√ pr x + q = 0 be real, then **

(a) p = q

(b) q

^{2}= pr

(c) p

^{2}= qr

(d) r

^{2}= pq

**Answer**

B

**Question. Which of the following is not a quadratic equation? **

(a) x^{2} – 2x + 2 (3 – x) = 0

(b) x (x + 1) + 1 = (x – 2) (x – 5)

(c) (2x – 1) (x – 3) = (x + 5) (x – 1)

(d) x^{3} – 4x^{2} – x + 1 = (x –2)^{3}

**Answer**

B

**Question. The equation 2x ^{2} + 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

**Answer**

D

**Question. If one root of 5x ^{2} + 13x + k = 0 be the reciprocal of the other root, then the value of k is **

(a) 0

(b) 1

(c) 2

(d) 5

**Answer**

D

**Question. The condition for one root of the quadratic equation ax ^{2} + bx + c = 0 to be twice the other, is **

(a) b

^{2}= 4ac

(b) 2b

^{2}= 9ac

(c) c

^{2}= 4a + b

^{2}

(d) c

^{2}= 9a – b

^{2}

**Answer**

B

**Question. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is **

(a) x^{2} – 6x + 6 = 0

(b) x^{2} + 6x – 6 = 0

(c) x^{2} – 6x – 6 = 0

(d) x^{2} + 6x + 6 = 0

**Answer**

A

**Question. If one root of the quadratic equation ax ^{2} + bx + c = 0 is the reciprocal of the other, then **

(a) b = c

(b) a = b

(c) ac = 1

(d) a = c

**Answer**

D

**Question. What is the speed of current ? **

(a) 20 km/hour

(b) 10 km/hour

(c) 15 km/hour

(d) 25 km/hour

**Answer**

B

**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

**Answer**

B

**Question. If (x-1/2) ^{2}−(x-3/2)^{2} =x+2 , then x = **

(a) 3

(b) 2

(c) 4

(d) None of these

**Answer**

C

**Question. If the equation (m ^{2} + n^{2}) x^{2} –2 (mp + nq) x + p^{2} + q^{2} = 0 has equal roots, then **

(a) mp = nq

(b) mq = np

(c) mn = pq

(d) mq = √np

**Answer**

B

**Question. If the ratio of the roots of the equation x ^{2} + bx + c = 0 is the same as that of x^{2} + qx + r = 0, then **

(a) r

^{2}b = qc

^{2}

(b) r

^{2}c = qb

^{2}

(c) c

^{2}r = q

^{2}b

(d) b

^{2}r = q

^{2}c

**Answer**

D

**Question. If a and b are the roots of the quadratic equation x ^{2} – 6x – 2 = 0 and if an = an – bn, then the value of a_{10}-2a_{g }/ 2a_{9} is **

(a) 6.0

(b) 5.2

(c) 5.0

(d) 3.0

**Answer**

D

**Fill in the Blanks :**

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

**Answer**

**two**

**Question. If r, s are roots of ax ^{2} + bx + c = 0, then is ………. **

**Answer**

**b ^{2} −2ac /c^{2}**

**Question. The equation ax ^{2} + bx + c = 0, a ≠ 0 has no real roots, if ……… **

**Answer**

**b ^{2} < 4ac**

**Question. A quadratic equation ax ^{2} + bx + c = 0 has two distinct real roots, if b^{2} – 4ac …………..**

**Answer**

**> 0**

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

**Answer**

**7 and –9**

**Question. If a, b are the roots of x ^{2} + x + 1 = 0, then a2 + b2 = ……….. **

**Answer**

**–1**

**True Or False :**

**Question. For the expression ax ^{2} + 7x + 2 to be quadratic, the possible values of a are non-zero real numbers. **

**Answer**

**True**

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

**Answer**

**False**

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

**Answer**

**True**

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

**Answer**

**False**

**Question. Sum of the reciprocals of the roots of the equation x ^{2} + px + q = 0 is 1/p.**

**Answer**

**False**

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