Question

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Answer 1

Answer:

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Answer 2

α and β are the zeros of x² - p(x + 1) - c

x² - p(x + p) - c = 0

x² - px - p - c = 0

x² - px - (p + c) = 0

comparing with general form of Quadratic Equation .

a = 1 , b = p , c = -(p + c)

α + β = -b/a = -(p)/1

α + β = -p

αβ = c/a = -(p + c) /1

αβ = -(p + c)

now, (α + 1) (β + 1) = α(β + 1) + 1(β + 1)

= αβ + α + β + 1

= αβ + (α + β) + 1

= -(p + c) + (-p)

= -p - c - p = -2p - c = - (2p + c)

Therefore, value for (α + 1) (β + 1) is - (2p + c)