Question

If product of zeros of polynomial
$ax {3} - 6x {}^{2} + 11x - 6$
is 4.Find
$a$
​

Answer 1

Answer

$\sf\frac{3}{2}$

$\rule{200}2$

Exlanation

Given, a polynomial p(x) = ax³ - 6x² + 11x - 6 with product of its zeroes as 4.

For a cubic polynomial, product of its zeroes = $\sf\frac{-d}{a}$

Where, d is the constant term of the polynomial and a is the coefficient of x³.

Here, constant term = -6

Product of zeroes = 4

Coefficient of x³ = a

Therefore,

4 = $\sf\frac{-(-6)}{a}$

⇒ 4 = 6/a

⇒ a = 6/4

⇒ a = 3/2

Answer 2

Answer:

$\huge\star\green{\underline{\mathfrak{Answer\::}}}$

Product of zeros of polynomial :-

$ax {}^{3} - 6x {}^{2} + 11x - 6 = 4$

Product of zeros= -d/a

d is a constant term.

Here, constant term is -6

So, 4 = -(-6)/a

or, 4 = 6/a

or, 4a = 6

Or, a = 6/4

So, a = 3/2 ★

Hope it helps you ♥ ♥ ♥