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Find all the zeros. Write the answer in exact form.

[tex] f(x) = x^3 - 5x^2 + 4x + 6 [/tex]

Sagot :

GinnyAnswer
To find the zeros of the polynomial function [tex]\( f(x) = x^3 - 5x^2 + 4x + 6 \)[/tex], we need to solve for the values of [tex]\( x \)[/tex] that make the function equal to zero, i.e., [tex]\( f(x) = 0 \)[/tex].

We start by writing the equation:
[tex]\[ x^3 - 5x^2 + 4x + 6 = 0 \][/tex]

To find the roots of this polynomial, we solve the equation using the standard methods for solving cubic polynomials.

Upon solving, we find the exact roots of the polynomial to be:
[tex]\[ x = 3, \quad x = 1 - \sqrt{3}, \quad \text{and} \quad x = 1 + \sqrt{3} \][/tex]

These are the zeros of the function [tex]\( f(x) = x^3 - 5x^2 + 4x + 6 \)[/tex].
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