Question

If one zeros of the Polynomial x² - 8x + k is seven times of the other find k

Answer 1

GIVEN :–

• A quadratic equation x² - 8x + k = 0.

• One zero is seven times of the other .

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

• Let the root of quadratic equation is α then other root is 7α .

• We know that –

$\\ \implies { \bold{Sum \: \: of \: \: roots = \dfrac{ - Coffieciant \: \: of \: \: x}{ Coffieciant \: \: of \: \: {x}^{2} } }}$

$\\ \implies { \bold{ \alpha + 7 \alpha = \dfrac{ - ( - 8)}{(1)}}}$

$\\ \implies { \bold{ \alpha + 7 \alpha = 8}}$

$\\ \implies { \bold{8 \alpha = 8}}$

$\\ \implies { \bold{ \alpha = \cancel \dfrac{8}{8} }}$

$\\ \implies \large { \boxed{ \bold{ \alpha = 1}}}$

• And –

$\\ \implies { \bold{product \: \: of \: \: roots = \dfrac{ Constant \: \: term}{ Coffieciant \: \: of \: \: {x}^{2} } }}$

$\\ \implies { \bold{ (\alpha)(7 \alpha) = \dfrac{k}{(1)}}}$

$\\ \implies { \bold{7 { \alpha }^{2} = k}}$

• Now put the value of 'α' –

$\\ \implies { \bold{7 {(1)}^{2} = k}}$

$\\ \implies \large{ \boxed{ \bold{ k = 7}}}$