find all the zeros of this equation

Question

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

Answer 1

-3x⁴ + 27x² + 1200 = 0

Divide each side by - 3

x⁴ - 9x² - 400 = 0

take t = x²

t² - 9t - 400 = 0

Using the factor method

t² - 25t + 16t - 400 = 0

Take out common term

t(t - 25) + 16(t - 25) = 0

Take out common factors

(t - 25)(t - 16) = 0

t - 25 = 0 or t  - 16 = 0

t = 25 or t = 16

Substitute  t = x²

x² = 25 or x² = 16

Take square root each side

x = √25 or x = √16

x = ± 5 or x = ±4

Therefore x = 4, 5, - 4, and - 5.

Comments

Typo mistake in 11 th line of above solution.

t(t - 25) + 16(t - 25) = 0

(t - 25)(t + 16) = 0

t - 25 = 0 or t  + 16 = 0

t = 25 or t = -16

Substitute  t = x²

x² = 25 or x² = - 16

x = √25 or x = √-16

Negitive squre root does not exist.

x = ± 5

Therefore, zeros are x =  5 and - 5.