If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the

1.	If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Answer» Given: -5 is a root of the quadratic equation 2x² + px – 15 = 0 Substitute the value of x = -5 2(-5)² + p(-5) – 15 = 0 50 – 5p – 15 = 0 35 – 5p = 0 p = 7 Again, In quadratic equation p(x² + x) + k = 0 7 (x² + x) + k = 0 (put value of p = 7) 7x² + 7x + k = 0 Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0 a = 7, b = 7, c = k Find Discriminant: D = b² – 4ac = (7)² – 4 x 7 x k = 49 – 28k Since roots are real and equal, put D = 0 49 – 28k = 0 28k = 49 k = 7 / 4 The value of k is 7/4.

If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.

Answer»

Given: -5 is a root of the quadratic equation 2x² + px – 15 = 0

Substitute the value of x = -5

2(-5)² + p(-5) – 15 = 0

50 – 5p – 15 = 0

35 – 5p = 0

p = 7

Again,

In quadratic equation p(x² + x) + k = 0

7 (x² + x) + k = 0 (put value of p = 7)

7x² + 7x + k = 0

Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0

a = 7, b = 7, c = k

Find Discriminant:

D = b² – 4ac

= (7)² – 4 x 7 x k

= 49 – 28k

Since roots are real and equal, put D = 0

49 – 28k = 0

28k = 49

k = 7 / 4

The value of k is 7/4.