MCQ Questions of Quadratic Equations with Answers

MCQ Questions with Answers during preparation and score maximum marks in the test. Students can prepare Class 10 Maths MCQ Questions of Quadratic Equations with answers from here and test their problem-solving abilities. Clear all the basics and get prepared completely for the test-taking assistance from Multiple choice Questions.

Students are educated to tackle the MCQ Questions for Class 10 Maths with answers to know different concepts. Practicing the Class 10 Maths MCQ Question will support your confidence in this manner assisting you with scoring admirably in the test.

Explore various MCQ Questions for Class 10 with answers provided with detailed solutions by looking beneath.

1. If the equation \(\mathrm{x^2} + 4x + k = 0\) has real and distinct roots, then

(a) k < 4
(b) k > 4
(c) k ≥ 4
(d) k ≤ 4

2. The equation \(\mathrm{x^2} – px + q = 0 \,p, q \in R\) has no real roots if :

(a) \(p^2 > 4q\)
(b) \(p^2 < 4q\)
(c) \(p^2 = 4q\)
(d) None of these

3. The roots of the equation \((b – c) x^2 + (c – a) x + (a – b) = 0\) are equal, then

(a) 2a = b + c
(b) 2c = a + b
(c) b = a + c
(d) 2b = a + c

4. The roots of quadratic equation \(5x^2 – 4x + 5 = 0\) are

(a) Real & Equal
(b) Real & Unequal
(c) Not real
(d) Non-real and equal

5. Equation \(\mathrm{(x+1)^2 – x^2 = 0}\) has _____ real root(s).

(a) 1
(b) 2
(c) 3
(d) 4

6. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

(a) 3
(b) 8
(c) 4
(d) 7

7. The product of two successive integral multiples of 5 is 300. Then the numbers are:

(a) 25, 30
(b) 10, 15
(c) 30, 35 (d) 15, 20

8. If \(\mathrm{p^2x^2 – q^2 = 0}\), then x =?

(a) ± q/p
(b) ±p/q
(c) p
(d) q

9. Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

(a) 14
(b) 16
(c) 15
(d) 18

10. Find a natural number whose square diminished by 84 is thrice the 8 more of given number

(a) 21
(b) 13
(c) 11
(d) 12

11. The roots of the quadratic equation \(x^2+14x+40=0\) are

(a) (4,10)
(b) (-4,10)
(c) (-4,-10)
(d) (4,-10)

12. Which one of the following is not a quadratic equation?

(a) \((x+2)^2=2(x+3)\)
(b) \(x^2+3x=(-1)(1-3x)^2\)
(c) \((x+2)(x-1)=x^2-2x-5\)
(d) \(x^3-x^2+2x+1=(x+1)^3\)

13.  Ram had scored 10 more marks in compare to Sita’s actual marks in mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

(a) 15 marks
(b) 10 marks
(c) 12 marks
(d) 20 marks

14. A bi-quadratic equation has degree

(a) 1
(b) 2
(c) 3
(d) 4

15. The quadratic equation \(2x^2 – 3x + 5 = 0\) has?

(a) Real and distinct roots
(b) Real and equal roots
(c) Imaginary roots
(d) All of the above

16. The cubic equation has degree

(a) 1
(b) 2
(c) 3
(d) 4

17. The sum of the roots of the quadratic equation \(3x^2 – 9x + 5 = 0\) is

(a) 3
(b) 6
(c) -3
(d) 2

18. If the roots of \(px^2 + qx + 2 = 0\) are reciprocal of each other, then

(a) P = 0
(b) p = -2
(c) p = ±2
(d) p = 2

19. The quadratic equation has degree

(a) 0
(b) 1
(c) 2
(d) 3

20. If the equation \(x^2 – bx + 1 = 0\) does not possess real roots, then

(a) – 3 < b < 3
(b) – 2 < b < 2
(c) b > 2
(d) b < – 2

Answers & Explanations

​1. Answer: (a) k < 4

Explanation: If roots of given equation are real and distinct then D = b² – 4ac > 0 

Here a = 1, b = 4 and c = k 

So, 

4² – 4 (1) (k) >0 

16 – 4k > 0 

16 > 4k 

K< 4

2. Answer: (b) \(p^2 < 4q\)

3. Answer: (d) 2b = a + c

4. Answer: (c) Not real

Explanation: To find the nature, let us calculate \(b^2 – 4ac\)

\(b^2 – 4ac = 4^2 – 4 \times 5 \times 5\)

= 16 – 100

= -84 < 0

5. Answer:(a) 1

Explanation: Since \(\mathrm{(x + 1)^2 – x^2 = 0}\)

\(\Rightarrow \mathrm{x^2 + 1 + 2x – x^2 = 0}\)

\(\Rightarrow\) 1 + 2x = 0

\(\Rightarrow\) x= -1/2

This gives only 1 real value of x.

6. Answer: (b) 8

Explanation: Let the number be x

Then according question,

x + 12 = 160/x

\(\mathrm{x^2 + 12x – 160 = 0}\)

\(\mathrm{x^2 + 20x – 8x – 160 = 0}\)

(x + 20) (x – 8) = 0

x = -20, 8

Since the number is natural, so we consider only positive value.

7. Answer:(d) 15, 20

Explanation: Let the consecutive integral multiple be 5n and 5(n + 1) where n is a positive integer.

According to the question:

5n × 5(n + 1) = 300

⇒ \(n^2\) + n – 12 = 0

⇒ (n – 3) (n + 4) = 0

⇒ n = 3 and n = – 4.

As n is a positive natural number so n = – 4 will be discarded.

Therefore the numbers are 15 and 20.

8. Answer:(a) ± q/p

Explanation: \(\mathrm{p^2x^2 – q^2 = 0}\)

⇒\(\mathrm{p^2x^2 = q^2}\)

⇒x = ±p/q

9. Answer: (c) 15

Explanation: Let her actual marks be x

Therefore,

\(\mathrm{9 (x + 10) = x^2}\)

⇒\(\mathrm{x^2 – 9x – 90 = 0}\)

⇒\(\mathrm{x^2 – 15x + 6x – 90 = 0}\)

⇒x(x – 15) + 6 (x – 15) = 0

⇒(x + 6) (x – 15) = 0

Therefore x = – 6 or x =15

Since x is the marks obtained, x ≠ – 6. Therefore, x = 15.

10. Answer: (d) 12

Explanation: \(x^2-84=3(x+8)\)
\(x^2−3x−108=0\)
\(x= 12\) or -9
So answer is 12

11. Answer: (c) (-4,-10)

Explanation: \(x^2+14x+40=0\)
\(x^2+4x+10x+40=0\)
\(x(x+4)+10(x+4)=0\)
\((x+4)(x+10)=0\)
\(x=-4 \,or-10\)

12. Answer: (c) \((x+2)(x-1)=x^2-2x-5\)

Explanation: We can expand each of these expression and compare with
\(ax^2+bx+c\)

13. Answer: (a) 15 marks

Explanation: \(9(x+10)=x^2\)
\(x^2-9x-90=0\)
\((x+6)(x-15)=0\)
Therefore, \(x = – 6\) or \(x =15\)

14. Answer: (d) 4

15. Answer: (c) Imaginary roots

16. Answer: (c) 3

17. Answer: (c) -3

18. Answer: (d) p = 2

19. Answer: (c) 2

20. Answer: (b) – 2 < b < 2

Explanation:​ If the equation does not possess real roots then 

d = b² – 4ac = 0 

Here a = 1, b = – b, c = 1 

d = b² – 4 < 0 

b² < 4 

b < \(\pm\)2

– 2 < b < 2