Question

If the product of two zeros of the polynomial f (x) = 2xZ³ + 6x² – 4x + 9 is 3, then its third zero is

A. \(\frac{3}{2}\)

B. - \(\frac{3}{2}\)

C. \(\frac{9}{2}\)

D. - \(\frac{9}{2}\)

Answer 1

Given;

f(x) = 2x³ + 6x² – 4x + 9

Product of the two zeros = 3

a = 2, 

 = 6,

c = – 4,

d = 9

Let the zeros of f(x) be p, q, r

Product of the zeroes = – d/a

p×q×r = – 9/2

3r = – 9/2 … (given p×q = 3)

r = – 3/2

Hence,

Third zero = – 3/2