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Exam practices for Asthmatic progression

Time: 50 Minutes                             Maximum Marks- 27

1.    Find the value of �k� for which the quadratic equation kx² – 5x + k = 0 have real roots.

(2 Marks)

2.    If – 4 is a root of the quadratic equation x² + px – 4 = 0 and x² + 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) x² – 2 (k – 1) x + 1 = 0.

(2 Marks)

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

        x² – 2ax + (a2 – b2) = 0

(3 Marks)

5.    For what value of k are the roots of the quadratic equation 3x² + 2kx + 27 = 0 real and equal?

(2 Marks)

6.    For what value of k are the roots of the quadratic equation kx² + 4x + 1 = 0 equal and real?

(2 Marks)

7.    Solve the following quadratic equation:

        2x² + 4x – 8 = 0

(4 Marks)

8.    Solve for x: 36x² – 12ax + (a² – b²) = 0.

(5 Marks)

9.    Solve: 16x² – 8a²x + (a⁴ – b⁴) = 0 for x.

(5 Marks)