Question

if alpha and beta are the zeros of the polynomial p(x) = x2- k(x+1) - m , show that (alpha +1 ) ( beta +1 ) = 1 - m

Answer 1

Step-by-step explanation:

here, p(x) = x^2 - sum of (alpha, beta) x + product of (alpha, beta)

so, here, k = alpha + beta

& alpha ×beta= - (k+m) = -k-m

we have to find,

(alpha +1 ) ( beta +1 ) = (alpha ×beta ) +alpha + beta + 1

= -k-m + k +1

= -m+1

= 1-m

hence, the proof