Question

Find all zeros of f(x) = x4 + 5x2 – 36 by completely factoring the polynomial.

f(x) = x4 + 5x2 – 36 = (x2 – 4) (x2 + 9) =

List the four zeros of the function.

Real zeros: +

Complex zeros:

Answer 1

Real Zeros x = ±4

Complex zeros : x = ±3 i

Explanation:

Explanation

f(x) = x⁴ + 5x² – 36

f(x) = x⁴ + 5x² – 36

= (x²)² + 9 x² - 4 x² - 36

= x² (x² + 9) - 4( x² +9)

= (x² -4 ) (x² +9)

f(x) = x⁴ + 5x² – 36 = (x² -4 ) (x² +9)

(x² -4 ) (x² +9) = 0

⇒ x² -4 = 0 and x² +9 =0

⇒ x² -2² = 0 and x² = -9

⇒ x = ±4 and x = ±3 i

Real Zeros x = ±4

Complex zeros : x = ±3 i