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

2x² + 2px — 15 = 0

Put x = –5

2(–5)² + 2p(–5) — 15 = 0

50 – 10p – 15 = 0

35 = 10p

p = 3.5

Equation p (x² + x) + k = 0 has equal roots i.e. d = 0

p (x² + x) + k = 0

p = 3.5

3.5 (x² + x) + k = 0

3.5x² + 3.5x + k = 0

d = b² – 4ac

d = (3.5)² – 4(3.5)(k)

d = 12.25 – 14k

Putting d = 0

∴ Equation will be:

0 = 12.25 – 14k

14k = 12.25

k = 0.875