Question

If a and ß are the zeros of the quadratic polynomial f(x) = x² - p(x + 1) – C, show that
(a + 1) (B + 1) = 1 - c.

Answer 1

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

& alpha*beta = 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

hope you understood