MCQ Class 10 Mathematics Quadratic Equations Nature of Roots

1. There will be total 30 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. The quadratic equation 2x² - 3x + 5 = 0 has

Real and distinct roots

Real and equal roots

Imaginary roots

All of the above

Your comments:

Question 1 of 30

2. The real roots of a quadratic equation

are given by

Your comments:

Question 2 of 30

3. The solutions of the quadratic equation

are

x = 2 and x = -5

x = 1 and x = -2

x = -2 and x = -5

x = 1 and x = 2

Your comments:

Question 3 of 30

4. The value of

for equation

Your comments:

Question 4 of 30

5. Which of the following is not a quadratic equation?

Your comments:

Question 5 of 30

6. For what value(s) of k will the equation kx²-5x+k=0 have a repeated root?

±5/2

5/2

-5/2

3/2

Your comments:

Question 6 of 30

7. A real number is said to be a root of ax²+bx+c =0

Your comments:

Question 7 of 30

-7/2

-3

Your comments:

Question 8 of 30

9. -3 is a root of the quadratic equation 2x² +px - 15 = 0. For what value of q , the equation p(x² + x ) + q= 0 has equal roots?

1/4

1/2

Your comments:

Question 9 of 30

10. The roots of x² - 8x + 12 = 0, are

x = 0

no real roots

real and unequal

real and equal

Your comments:

Question 10 of 30

11. If

is a root of the equation x²+kx -

=0, then the other root of the quadratic equation is

-2

1/4

-5/2

1/2

Your comments:

Question 11 of 30

12. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Find their present ages

2 and 18

The situation is not possible

6 and 14

10 and 10

Your comments:

Question 12 of 30

13. The nature of the roots of following quadratic equation

Unequal

Equal

No real roots

None of above.

Your comments:

Question 13 of 30

14. If the equation px² – 6x – 2 = 0 has real roots then, ________

Your comments:

Question 14 of 30

15. The positive value of k, for which both equations: x2 + kx + 64 = 0 and x2 - 8x + k = 0 have real roots is________

k ≤ 16

k = -16

k ≥ 16

k = 16

Your comments:

Question 15 of 30

16. If one root of a Quadratic equation is m + , then the other root is

m - √n

m +√n

Can not be determined

√m + n

Your comments:

Question 16 of 30

17. The positive value of k, for which both equations: x² + kx + 64 =0 and x² - 8x + k =0 have real roots is___________

Your comments:

Question 17 of 30

18. If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are

Distinct, Rational

Same Irrational

Distinct, Irrational

Same, Rational

Your comments:

Question 18 of 30

19. If the equation px² - 6x - 2 = 0 has real roots then, ________

Your comments:

Question 19 of 30

20. Write the condition, when given quadratic equation has real and distinct roots

Your comments:

Question 20 of 30

21. Comment on the nature of the roots of the equation

Real and distinct roots

Real and equal roots

Imaginary roots

None of the above

Your comments:

Question 21 of 30

22. The roots of the equation x2 - 3x - m (m + 3) = 0, where m is a constant, are

–m, m + 3

m, m + 3

–m, - (m + 3)

m, - (m+3)

Your comments:

Question 22 of 30

23. If the equation 9x² – 6x + c = 0 has equal roots then, the value of c is

Your comments:

Question 23 of 30

24. If -3 is a root of both the Quadratic equations 2x2 + px - 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is.

1/2

1/4

Your comments:

Question 24 of 30

25. If a,b,c are real and b²-4ac >0 then roots of equation are

real roots

real and equal

real and unequal

No real roots

Your comments:

Question 25 of 30

26. The quadratic equation whose roots are real and equal is:

x² - 4x + 4 = 0

2x² - 4x + 3 = 0

x² - 2 √2 - 6 = 0

3x² - 5x + 2 = 0

Your comments:

Question 26 of 30

27. Write the condition, when given quadratic equation has no real roots.

Your comments:

Question 27 of 30

28. Which of the following equations has two distinct real roots?

x² + x - 5 = 0

2x² - 3√2 x + 9/4 = 0

x² + 3x + 2√2 = 0

5x² - 3x + 1 = 0

Your comments:

Question 28 of 30

29. If the equation

= 0 has equal roots then, the value of c is

20, 22

22, 24

Your comments:

Question 29 of 30

30. Which of the following is a solution of the quadratic equation

Your comments:

Question 30 of 30

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