. 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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