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Question

# If a,b and c are three nonzero numbers and the polynomial p(x) = x3 + ax2 + bx - c factors as (x - a) (x - b ) (x - c ), then the value of p(3) is

A

16

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B

32

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C

0

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D

9

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Solution

## The correct option is B 32 1.x3 + ax2 + bx - c = (x - a) (x - b ) (x - c ) where a,b,c are non-zeros, Comparing the coefficients on both sides, we get a = a + b + c ; => b + c = 0 (1) b = ab + bc + ca (2) c = abc => ab = 1 (3) Using (3) in (2), 1 + c (a + b ) = b. Now p (a) = 0 à a3 - a3 + ab - c = 0 ðc = 1 à b = - 1 à a = - 1 . ∴ p(3) = (3 - a) . (3 - b) . (3 - c) = 4 * 4 * 2 = 32.

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