if alpha and beta are zeroes of F(x)=X^2-P(x+1)-c show that (alpha+1)into (beta +1)=1-c

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Solution

Given that alpha and beta are the roots of the quadratic equation f(x) = x^2-p(x+1)-c = x^2-px-p-c = x^2 -px-(p+c),
comparing with ax^2 + bx + c, we have, a =1 , b= -p & c= -(p+c)
alpha+beta = -b/a = -(-p)/1 = p
& alphabeta = c/a = -(p+c)/1 = -(p+c)
Therefore, (Alpha + 1)(beta+1)
= Alpha*beta + alpha + beta + 1
= -(p+c) + p + 1
= -p-c+p+1
= 1-c

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