**Class X Math**

Test For QUadratic Equations

**Total Marks: 30**

**Total Time: 60 min**

**1.** Find the value of �k� for which the quadratic equation kx^{2} – 5x + k = 0 have real roots.

**(2 Marks)**

**2.** If – 4 is a root of the quadratic equation x^{2} + px – 4 = 0 and x^{2} + px + k = 0 has equal roots, find the value of k.

**(2 Marks)**

**3.** For what value of k, does the given equation have real and equal roots?

(k + 1) x^{2} – 2 (k – 1) x + 1 = 0.

**(2 Marks)**

**4.** Using quadratic formula, solve the following quadratic equation for x:

x^{2} – 2ax + (a2 – b2) = 0

**(3 Marks)**

**5.** For what value of k are the roots of the quadratic equation 3x^{2} + 2kx + 27 = 0 real and equal?

**(2 Marks)**

**6.** For what value of k are the roots of the quadratic equation kx^{2} + 4x + 1 = 0 equal and real?

**(2 Marks)**

**7.** Solve the following quadratic equation:

2x^{2} + 4x – 8 = 0

**(3 Marks)**

**9.** Solve for x: 36x^{2} – 12ax + (a^{2} – b^{2}) = 0.

**(5 Marks)**

**10.** Solve: 16x^{2} – 8a^{2}x + (a^{4} – b^{4}) = 0 for x.

**(5 Marks)**