Question

if alpha and beta are the zeroes of the polynomial p(x)=x2-k(x+1)-a and (alpha+1)(beta+1)=0 find a

Answer 1

Alpha and beta are the roots of P(x) =
x²-k(x+1)-a,

Given that,

(Alpha +1) (beta+1) = 0,
=> Either alpha +1 = 0 or beta +1 = 0,
=> Either alpha = -1 or beta = -1,
=> Atleast one of the root of P(x) is -1,
Substitute it in P(x)

=> P(-1) = 0 = (-1)²-k(-1+1) - a,
=> 0 = 1 +0 - a
=> a = 1,

Therefore the value of a = 1,

hope you understand !!!

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