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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:

Respuesta :

Answer:

Real Zeros    x = ±4

Complex zeros :  x = ±3 i

Step-by-step 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

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