Question

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 1

Given equation

px(x-3) + 9 = 0

px^2 - 3px + 9 = 0

As roots are equal then determinant D should be equal to 0.

We know, D = b^2 - 4ac

Then,

(-3p)^2 - 4*p*9 = 0

9p^2 - 36p = 0

p(p - 4) = 0

p = 0, 4

0 value not possible

Therefore value of p = 4