Question

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

x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10

Answer 1

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

Answer 2

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 √(5)\\\\ x=√(-100)`

The factor of the equation is

`x=\pm √(5)\\\\ x= \pm 10i`

Hence proved