Question

if alpha and beta are the zeros of the polynomial x

-p (x + 1) -c then (alpha +1) (beta + 1)is equal to​

Answer 1

I have attached the solution.

Answer 2

Given : α and β are zeroes of the polynomial

x² - p(x + 1) - c

To Find : (α + 1)(β + 1)

Solution:

polynomial x² - p(x + 1) - c

= x² - px - p  - c

= x² - px - (p + c)

Sum of zeroes = α +  β  = -(-p)/1 = p

Product of zeroes  = αβ =  -(p + c)/1 = - (p + c)

(α + 1)(β + 1)

= αβ + α +  β + 1

=  - (p + c) + p  + 1

= -c + 1

= 1 - c

(α + 1)(β + 1) = 1 - c

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