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

Question 1 of 30

2. The real roots of a quadratic equation

are given by

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

Question 3 of 30

4. The value of

for equation

Question 4 of 30

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

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

Question 6 of 30

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

Question 7 of 30

-7/2

-3

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

Question 9 of 30

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

x = 0

no real roots

real and unequal

real and equal

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

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

Question 12 of 30

13. The nature of the roots of following quadratic equation

Unequal

Equal

No real roots

None of above.

Question 13 of 30

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

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

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

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___________

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

Question 18 of 30

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

Question 19 of 30

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

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

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)

Question 22 of 30

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

Question 23 of 30

24. If -3 is a root of both the Quadratic equations 2×2 + 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

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

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

Question 26 of 30

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

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

Question 28 of 30

29. If the equation

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

20, 22

22, 24

Question 29 of 30

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

Question 30 of 30