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

Answer:

$x=+10i,-10i,\sqrt{5} ,-\sqrt{5}$

Step-by-step 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'

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

$x^2=5, x=+-\sqrt{5}$