Question

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

Answer 1

-5 is a root of 2x^2+px-15 = 0.
Substituting x = -5 we get
2(-5)^2+p(-5)-15 = 0
2(25)-5p-15 = 0
50-5p-15 = 0
5p = 50-15 = 35
p = 7 (1)
So the quadratic equation p(x^2+x) + k = 0 becomes after substituting p =7 from (1)
7(x^2+x) + k = 0
7x^2+7x+k = 0
We know that a quadratic has equal roots if D = b^2-4ac = 0
Here a = 7, b = 7 and c = k
=> D = 7^2 -4(7)(k) = 0
=> 49 -28k = 0
=> k = 49/28
= 7/4
Answer: k = 7/4