Question

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

Answer 1

Given

The equation in the form

$x^{4}+95x^{2}-500 =0$

Find the factor of the above equation

To proof

factoring the above equation

we get

$x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0$

now sloving the equation we get the value

x² = 5

x² = -100

$x =\pm \sqrt{5}\\\\ x=\sqrt{-100}$

The factor of the equation is

$x=\pm \sqrt{5}\\\\ x= \pm 10i$

Hence proved

Answer 2

X= the square root of 5
x= the square root of -5
x=10i
x=-10i