Factor this equation to find zeros.

Question

Find all zeros of this equation: x^4 +x^2 -72 =0.

1. Add + and -
2. Simplify radicals.
3. Enter exact values, no decimal approximations.
4. Use i for imaginary solutions.

Answer 1

x⁴ + x² - 72 = 0

Let u = x², so u² = x⁴

x⁴ + x² - 72 = 0

u² + u - 72 = 0

(u+9)(u-8) = 0

u = -9 and 8

u = x² = -9

x = +/- 3i

u = x² = 8

x = +/- sqrt(8) = +/- 2sqrt(2)

4 zeros at x = +/- 3i and +/- 2sqrt(2)