Choose the correct option from the given below options by solving the following question:
If α, β are the zeros of the polynomial f(x) = x² - p(x + 1) - c = 0 such that (α + 1)(β + 1) = 0, then c = ?
Approved Tutor Answer11 Months agoTo solve the problem, we start with the polynomial given by:
f(x) = x² - p(x + 1) - c
We know that the zeros of this polynomial are α and β. The condition given is:
(α + 1)(β + 1) = 0
This implies that either α + 1 = 0 or β + 1 = 0. Therefore, we can conclude that:
Now, substituting α = -1 into the polynomial:
f(-1) = (-1)² - p(-1 + 1) - c = 0
This simplifies to:
1 - p(0) - c = 0
Since p(0) = 0, we have:
1 - c = 0
Thus, we find:
c = 1
Therefore, the correct option is:
A. 1
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