CBSE Test Paper Chapter 4 : Quadratic Equations

CBSE TEST PAPER MATHEMATICS (Class-10)Chapter 4 : Quadratic Equations

1. Find the value of k for  kx² + 2x - 1 = 0, so that it has two equal roots

2. Find the value of k for  k x²   - 2√ 5 x + 4 = 0, so that it has two equal roots.

3. If the roots of the equation (b - c) x² + (c - c) x + (a - b) = 0 are equal, accordingly prove that
2b = a + c.

4. Find the discriminant of the quadratic equation 3x²– 4 √3 x + 4 = 0, and hence find the nature of its roots.

5. Find the value of k for  2 x² + k x + 3 = 0, so that it has two equal roots.

6. Find the value of k for     k x (x – 2) + 6 = 0, so that it has two equal roots.

7. Find the value of k for which the equation x² + 5kx + 16 = 0 has no real roots.

8 Find the discriminant of the quadratic equation 2x²– 6x + 3 = 0, and hence find the nature of its roots.

9. Find the value of k for   k² x² –  2 (2 k - 1) x + 4 = 0, so that it has two equal roots.

10. Find the value of k for (k + 1) x²  – 2 ( k - 1) x + 1= 0, so that it has two equal roots.

11. Determine the positive value of k for which the equation x² + k x + 64 + 0 and x² – 8x + k = 0 will both have real roots.

12. Find the discriminant of the quadratic equation 2x² – 3 x + 5 = 0, and hence find the nature of its roots.

13. Find the value of k for x² – 2(k + 10x + k² ) = 0, so that it has two equal roots.
14. If - 4 is a root of the quadratic equation x² + px–4=0 and the quadratic equation x²+ px +k=0 has equal roots, find the value of k.

15. Find the discriminant of the quadratic equation 2x² – 4x + 3 = 0, and hence find the nature of its roots.

16. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.


17. In a class test, the sum of Amit’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 Marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

18. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

19. A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

20. Two water taps together can fill a tank in 9 ³/₈  hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.