Question

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

Answer 1

2x^2+px-15=0

p (x^2+x)+k=0

since -5 is the root of both equations

2 (-5)^2+p(-5)-15=0

50-5p-15=0

5p=35

p=7

In equation (II)

7 [(-5)^2 +(-5)]+k=0

7(20)+k=0

140+k=0

k=-140

so k=-140. & p=7