if -5 is a root of the quadratic equation 2x2+px-15=0 and the quadratic equation p(x2+x)+k=0 has equal rootrs, find the value of k.
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let f(X) = 2x² +px -15
if -5 is it's root thus
f(-5) = 0 = 2(-5)²+p(-5)-15
= > 50-15 = 5P
=>
P= 7
let g(X) = p(x²+x) +k
g(X) = 7(x²+X)+k = 7x²+7x+k
a= 7
b = 7
c = k
has equal roots thus
b²-4ac = 0
49-28k = 0
k = 49/28
k = 7/4
if -5 is it's root thus
f(-5) = 0 = 2(-5)²+p(-5)-15
= > 50-15 = 5P
=>
P= 7
let g(X) = p(x²+x) +k
g(X) = 7(x²+X)+k = 7x²+7x+k
a= 7
b = 7
c = k
has equal roots thus
b²-4ac = 0
49-28k = 0
k = 49/28
k = 7/4
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