Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = x² - p(x + 1) - c
= x² - px - p - c ← in standard form
with a = 1, b = - p and c = - p - c
Given that α and β are the zeros of f(x), then
α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex], thus
α + β = - [tex]\frac{-p}{1}[/tex] = p , and
αβ = [tex]\frac{-p-c}1}[/tex] = - p - c
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(α + 1)(β + 1) ← expand factors
= αβ +α + β + 1 ← substitute values from above
= - p - c + p + 1
= - c + 1 = 1 - c ← as required
