How would you find the zero of [tex] f(x) = 16x^4 - 9x^2 [/tex]?

f ( x ) = 16 x 4 − 9 x 2 16 x 4 − 9 x 2 = 0 x 2 ( 16 x 2 − 9 ) = 0 x 2 = 0 or 16 x 2 − 9 = 0 x = 0 or ( 4 x − 3 ) ( 4 x + 3 ) = 0 x = 0 or 4 x − 3 = 0 or 4 x + 3 = 0 x = 0 or 4 x = 3 / : 4 or 4 x = − 3 / : 4 x = 0 or x = 4 3 ​ or x = − 4 3 ​

Answered by Lilith | 2024-06-10

f ( x ) = 16 x 4 − 9 x 2 f ( x ) = 0 ⟺ 16 x 4 − 9 x 2 = 0 x 2 ( 16 x 2 − 9 ) = 0 ⟺ x 2 = 0 ∨ 16 x 2 − 9 = 0 x = 0 ∨ 16 x 2 = 9 x = 0 ∨ x 2 = 16 9 ​ x = 0 ∨ x = − 16 9 ​ ​ ∨ x = 16 9 ​ ​ x = 0 ∨ x = − 4 3 ​ ∨ x = 4 3 ​

Answered by Anonymous | 2024-06-10

To find the zeros of f ( x ) = 16 x 4 − 9 x 2 , we factor the equation to x 2 ( 16 x 2 − 9 ) = 0 . The solutions are x = 0 , x = 4 3 ​ , and x = − 4 3 ​ .
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Answered by Lilith | 2024-12-23