Question

Please solve this for me T_T

If

`x - √(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

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

Explanation:

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

if
`x-√(a)` is a factor of this expression it means that
`√(a)` is a root of it

it comes

`2*(√(a))^4-2*a^2*(√(a))^2-3*√(a)+2*(√(a))^3-2(√(a))^2+3=0`

So

`2*a^2-2*a^3-3*√(a)+2*a*√(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