Question

please solve this for me T_T
If
$x - \sqrt{a}$
is a factor of
$2 {x}^{4} - 2 {a}^{2} {x}^{2} - 3 {x} + 2 {a}^{3} - 2 {a}^{2} + 3$
then find the value of
$a$
​

Answer 1

Answer:

$\boxed{\sf \ a = 1 \ }$

Step-by-step explanation:

let s assume that a >=0 so that we can take the square root

if $x-\sqrt{a}$ is a factor of this expression it means that $\sqrt{a}$ is a root of it

it comes

$2*(\sqrt{a})^4-2*a^2*(\sqrt{a})^2-3*\sqrt{a}+2*(\sqrt{a})^3-2(\sqrt{a})^2+3=0$

So

$2*a^2-2*a^3-3*\sqrt{a}+2*a*\sqrt{a}-2*a+3=0$

we can notice that 1 is a trivial solution as

2-2-3+2-2+3=0

so the answer is 1

let s double check

if a =1

the expression is

$2x^4-2x^2-3x+2-2+3=2x^4-2x^2-3x+3$

and we can write

$2x^4-2x^2-3x+3=(x-1)(2x^3+2x^2-3)$

so 1 is the correct answer