Question

Find all the zeros of the equation.

Answer 1

You can either use the Pythagorean theorem right away (a = -3, b = 27, c = 1200) or Try factoring the polynomial to find the zeros.

I would factor and start by dividing everything by -3.

-3x^4 + 27x^2 + 1200 = 0
-3(x^4 - 9x^2 - 400) = 0

If you divide by -3 on both sides you see that the -3 is now gone. 0/-3 = 0

x^4 - 9x^2 - 400 = 0
factor further or use Pythagorean theorem.

(x² - 25)(x² + 16) = 0

Solve for the x-values by setting each one equal to zero.

x² - 25 = 0
x² = 25
x is +5 or -5

x² + 16 = 0
x² = -16
x = √(-16)
Two non-real solutions
x is +4i or -4i