Question

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

Answer 1

2×(-5)×(-5)+p(-5)-15=0

50+75p=0
75p= -50
p= -50/75

now put value of in 2nd eq
and used formula
D=b×b-4bc

Answer 2

-5 is the root of the equ
so 2×-5 square +p×-5-15=0
p=15-50/-5=7
now
7×(x square +x)+k=0
7x square +7x+k=0
for equal root D=0
D=b square -4ac=0
49-28k=0
k=-49/-28
k=7/4