Question

question no. 15, solve it will give you 100 points​

Answer 1

Answer:

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Answer 2

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For a general Quadratic polynomial say

P(x) = ax² + bx + c

Alfa + Beta = -b/a

And

Alfa × Beta = c/a

Given Quadratic polynomial is

F(x) = x² - p(x + 1) - c

F(x) = x² - px -(p + c)

Alfa + Beat = p And

Alfa × Beta = -(p + c)

To prove (Alfa + 1) (Beta + 1) = 1 - c

L.H.S

(Alfa + 1) (Beta + 1) = z let

z = (Alfa × Beta) + (Alfa + Beta) + 1

z = -(p + c) + p + 1

z = - p - c + p + 1

z = 1 - c

So,

(Alfa + 1) (Beta + 1) = (1 - c)

Hence proved!!)