Question

if the sum of the zeros of the cubic polynomial 4 x square minus kx square minus 8 x minus 12 is minus 3 by 4 then the value of k is

Answer 1

Solution :-

Given Polynomial :-

4x³ - kx² - 8x -12

Given sum of roots

$=\dfrac{-3}{4}$

Now as in a cubic polynomial :-

Sum of roots :-

= -b/a

= α + β + γ

Sum of Product of roots taken two at a time :-

= c/a

=αβ + βγ + αγ

Product of roots

= -d/a

= αβγ

So we are provided with

a = 4

b = -k

c = -8

d = -12

and

$\alpha + \beta + \gamma=\dfrac{-3}{4}$

So we have

$\dfrac{-b}{a} = \dfrac{-3}{4}$

$\implies \dfrac{-(-k)}{4} = \dfrac{-3}{4}$

$\implies \dfrac{k}{\cancel{4}} = \dfrac{-3}{\cancel{4}}$

$\implies k = -3$

$\Huge{\boxed{\sf{Value\: of\: k = -3 }}}$