Question

a
find the value of a
x³—2ax²+16​

Answer 1

Answer:

use factor theorem as x+2 is factor of

x³-2ax²+16 so put x = -2 and equate the equation to 0

so putting x = -2

(-2)³-2a(-2)²+16 =0

-8-8a+16=0

-8a = -8

a = 8/8= 1

So,

a = 1

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Answer 2

${ \tt{ \large \underline{question \colon}}}$

${ \rm{ {x}^{3} - 2a {x}^{2} + 16 \: find \: the \: value \: of \: a}}$

${ \tt{ \large \underline{to \: find \colon}}}$

${ \rm{ \longrightarrow to \: find \: the \: value \: of \: a}}$

${ \tt{ \large \underline{solution \colon}}}$

${ \rm{according \: to \: factor \: theoram}}$

${ \rm{let \: x + 1 = 0}}$

${ \rm{\implies x = - 1}}$

${ \rm{ \therefore {x}^{3} - 2a {x}^{2} + 16 = 0}}$

${ \rm{ \implies {( - 1)}^{3} - 2a {( - 1)}^{2} + 16 = 0}}$

${ \rm{ \implies - 1 - 2a + 16 = 0}}$

${ \rm{ \implies - 2a + 15 = 0}}$

${ \rm{ \implies ( - 2a) = ( - 15)}}$

${ \rm{ \implies ( \not- 2a) = ( \not- 15)}}$

${ \rm{ \implies 2a = 15}}$

${ \rm{ \implies a = \dfrac{15}{2} }}$

${ \rm{ \implies a = 7.5 }}$

${ \tt{ \large{ \therefore the \: value \: of \: a = 7.5 }}}$