Question

if -5 is the root of the quadratic equation 2 X square + px - 15 is equal to zero and the quadratic equation p(x2+x)+k is equal to zero has equal roots find the value of k

Answer 1

putting X= -5 in given quadratic equation

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

50-5p-15=0

35-5p=0

35=5p

p=7

Substituting p=7 in 2nd polynomial

7(x^2+x)+K

7x^2 + 7x + k

for equal roots D=0

B^2 - 4AC = 0

(7)^2 - 4*7*k = 0

49 - 28k = 0

49 = 28k

divide by 7 both sides

7= 4k

k = 7/4