Question

If alpha and 1/alpha are zeros of the polynomial 4xsq -2x+(k-4)find k

Answer 1

AnswEr:

Value of k is 8.

ExplanaTion:

Given Polynomial :

• 4x² - 2x + (k - 4)

Zeroes :

• $\alpha$

• $\dfrac{1}{\alpha}$

We know that,

$\large{\boxed{\sf{\red{Product\:of\:zeroes\:=\:\dfrac{c}{a}}}}}$

: $\implies$ $\sf{\alpha \times \dfrac{1}{\alpha}}$ = $\sf{\dfrac{k\:-\:4}{4}}$

: $\implies$ 1 = $\sf{\dfrac{k\:-\:4}{4}}$

: $\implies$ 4 = k - 4

: $\implies$ k = 4 + 4

: $\implies$ k = 8

$\therefore$ Value of k is 8.

Answer 2

$\tt{ \purple{ \implies{f(x) = 4 {x}^{2} - 2x + (k - 4) }}}$

$\alpha + \dfrac{1}{ \alpha }= \dfrac{ - b}{a} = \dfrac{1}{2}$

$1 = \dfrac{c}{a} = \dfrac{k - 4}{4}$

$\implies k = 8 .........(A)$