Question

If the product of zeros of the polynomial $f(x)=2x^{3}+6x^{2}-4x+9$ 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

SOLUTION :  

The correct option is (b) : -3/2

Let α,β,γ are the three Zeroes of the cubic polynomial and αβ = 3 .

Given : f(x) = 2x³ + 6x² - 4x + 9

On comparing with ax³ + bx² + cx + d ,

a = 2 , b = 6 , c = - 4 , d = 9

Product of zeroes of cubic polynomial = - constant term /coefficient of x³

αβγ = −d/a

3(γ) = - 9/2

γ = -9/2 × ⅓

γ = - 3/2

Hence, the value of third zero (γ) is - 3/2 .

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Answer 2

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