Question

If a and ß are the zeroes of the quadratic polynomial f(x) = x2 - (x + 1) - C, Show
that (a + 1) (B + 1) = 1 - c.​

Answer 1

Hey!

___________________

Given,

Alpha and beta are the zeroes of the quadratic polynomial x^2 - p (x + 1) - c

Alpha ( @ ) 

Beta ( ß )

x^2 - p ( x + 1 ) - c

x^2 - px - p - c

x^2 - px - (p+c)

Comparing with ax^2 + bx + c

a = 1

b = - p

c = - (p+c)

We know,

Alpha + Beta = - b/a = - (-p) = p

Alpha × Beta = c/a = - ( p+c ) 

Thus,

( Alpha + 1 ) ( Beta + 1 ) 

= @ß + @ + ß + 1

= - (p+c) + p + 1

= - p - c + p + 1

= 1 - c

Thus, ( Alpha + 1 ) ( Beta + 1 ) = 1 - c

Mark me as brainliest and Hope it helps :)