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
• B. 32
• C. 0
• D. 9

Answer 1

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.