Question

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

Answer 1

2x^2-px-15=0
2(-5)^2-5p-15=0
2×25-5p-15=0
50-15=5p
35/5=p
p=7

p(x^2+x)+k=0
px^2+px+k=0
7x^2+7x+k=0

The quadratic equation has equal roots
D=b^2-4ac=0
(7)^2-4×7×k=0
49-28k=0
7(7-4k)=0
7-4k=0
7=4k
k=7/4
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