Question

if alpha and beta are zeros of the polynomial x square - 3 bracket open X + 1 bracket close + c such that alpha + 1 Oz into beta + 1 is equal to zero then find the value of c

Answer 1

X ^2 - 3(x+1) +c is d given equation
Alpha and beta are roots
First d equation is expanded to x^2 - 3x +(-3+c) by opening the bracket.
Now... Alpha + beta = (-b/ a)
And alpha * beta = (c/a)... where a=1, b=-3, c=-3+c frm d equation above
So.. As given.. (alpha +1) (beta + 1)= alpha* beta +alpha+ beta+1 = 0
=)alpha * beta +(alpha + beta) +1 =0
=)-3+c+3+1 = 0
=)c+1 =0
=)c = - 1