. If alpha, beta are the zeros of the polynomial
polynomial f(x) = x^2 - p(x + 1) - c = 0 such (alpha + 1)(beta + 1) = 0 , then c =
A: 1
B: 0
C: - 1
D: 2
Best Answer
Explanation:
If and are the zeroes of the polynomial x2- p(x + 1) - c, find the value of ( + 1)( + 1)
x2- p(x + 1) - c = x2- px - p - c
If we compare with ax2+ bx + c, we get a = 1 , b = -p and c = -(p + c)
Since, α and β are the zeroes of the given polynomial.
Thus,
α + β = -b/a = -(-p)/1 = p and αβ = c/a = -p - c / 1 = -p - c
Therefore, in order to find (α + 1)(β + 1) = 0
(α + 1)(β + 1) = αβ + α + β + 1
= - p - c + p + 1
= 1 - c
Final Answer:
The value of ‘c’ equals 1.
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