Question

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

Answer 1

(x2+100) • (x2-5) so this would be the optimal answer

Answer 2

`x=+10i,-10i,√(5) ,-√(5)`

Explanation:

`x^4 + 95x^2 -500 = 0`

REwrite the equation in the form of quadratic equation ax^2+bx+c=0

To solve for x , we replace x^2 by 'u'

`u^2 + 95u -500 = 0`

Now we factor the left hand side

Product is -500 and sum is 95

100 times -5 is -500

100 + (-5) is 95, factors are 100 and -5

`u^2 + 95u -500 = 0`

`(u+100)(u-5) = 0`

Replace u with x^2

`(x^2+100)(x^2-5) = 0`

Set each factor =0 and solve for x

`x^2+100= 0, x^2=-100`

`x^2-5= 0, x^2=5`

To remove square , take square root on both sides

square root (-1) is 'i'

`x^2=-100, x= +-10i`

`x^2=5, x=+-√(5)`