Question

What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve

Answer 1

x4-5x2-14=0

Four solutions were found :

x = ± √7 = ± 2.6458
x= 0.0000 - 1.4142 i
x= 0.0000 + 1.4142 i
Step by step solution :

Answer 2

The given equation is :
`x^(4) -5x^(2)-14=0`

Let
`x^(2) =y`

The given equation reduces to :

`y^(2)-5y-14=0.`

Factoring the equation we have:

(y-7)(y+2)=0

Solving the equations for y:

y-7=0 y+2=0

Or y=7. Or y=-2.

Substituting y value:

`x^(2) =7`
`x^(2) =-2`

Or x=+2.64,-2.64. Square root of negative number is not real. x=
`√(-2) =+i√(2) ,-i√(2)`

X= -2.64,+2.64,
`i√(2) ,-i√(2)`