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Answer :
The zeros of [tex]f(x) = x^3 + 5x^2 - 9x - 45[/tex] are x = -3, -5, 3, found using the Rational Root Theorem and factoring.
To find the zeros of the cubic function [tex]f(x) = x^3 + 5x^2 - 9x - 45[/tex], we need to solve for x when f(x) = 0. One approach is to use methods like factoring, synthetic division, or numerical methods.
Factoring directly might be complex for this cubic. Instead, consider using the Rational Root Theorem to identify potential roots. The theorem suggests testing divisors of the constant term (45) by divisors of the leading coefficient (1). By testing values, you find that x = -3 is a root.
Using synthetic division or polynomial long division, divide f(x) by (x + 3). The resulting quotient is a quadratic, which can be factored to find the other roots: x = -3, -5, 3.
Therefore, the zeros of f(x) are x = -3, -5, 3.
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