The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i
How to find equivalent equation?
The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore,
f(x) = 16x⁴ - 81 = 0
Hence,
9 × 9 = 81
4x² × 4x² = 16x⁴
Therefore,
16x⁴ - 81 = (4x² + 9)(4x² - 9)
Hence,
The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).
The zero's of the function are as follows:
4x² = 9
x² = 9 / 4
x =± 3 / 2
4x² = -9
x² = - 9 / 4
x =√-9 / 2
x = ± 3 / 2i
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