Find all the zeros of the equation.

Question

-3x^4+27x^2+1200=0

I know the zeros are –5, 5, –4i, and 4i, but how do I get there?

Answer 1

- 3 x⁴ + 27 x² + 1200 = 0

- 3 ( x⁴ - 9 x² - 400 ) = 0

Divide both sides by - 3

x⁴ - 9 x² - 400 = 0

( x⁴ - 25 x² ) + ( 16 x² - 400 ) =

x² ( x² - 25 ) + 16 ( x² - 25 ) =

( x² - 25 ) ( x² + 16 ) =

( x + 5 ) ( x - 5 ) ( x² + 16 ) = 0

The equation will be equal to zero when the expressions in parentheses are equal to zero.

This means that you have three conditions.

First condition:

x + 5 = 0

Subtract 5 to both sides

x = - 5

Second conditiion:

x - 5 = 0

Add 5 to both sides

x = 5

Third condition:

x² + 16 = 0

Subtract 16 to both sides

x² = - 16

x = ± √ - 16

x = ± 4 i

So the solutions are:

x = - 5 , x = 5 , x = 4 i , x = 4 i

Answer 2

Thank you!