Question

if-5 is the root of eq 2x2+px-15=0 and the quadratic eq p(x2+x)+k=0 has eq root find k

Answer 1

f(x) = 2x^2 + px - 15
f(-2) = 2*(-2)^2 + p*(-2) - 15 = - 2p-7
Since - 2 is a root, f(-2)=0 => p = - 7/2
So (-7/2)(x^2 +x) + k = 0 has equal roots
So - 7x^2 - 7x + 2k = 0 has equal roots
So (-7)^2 + 4*7*2k = 0
=> 49 +56k =0
=> k = - 49/56 = - 7/8

Answer 2

See the solution in picture
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