If one root of a quadratic equation 2x² + px – 15 = 0 is –5 and the root of the quadratic equation p(x² + x) + k = 0 are equal then find the value of k.

Since -5 is the zero of the first equation,

Put x = -5 in first equation

2(-5)² + p (-5) – 15 = 0

2× 25 – 5p – 15 = 0

5p = 50 – 15

5p = 35

p = 7

If the roots are equal, then

b² – 4ac = 0

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

∴ a = p = 7

b = p = 7

c = k

(7)² – (4 × 7 × k) = 0

(7)² – 28 k = 0

28k = 49

k = 49 / 28

k = 7 / 4