MHB Polynomial Function: Find All Zeros (Real & Complex)

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The discussion focuses on finding all zeros of the polynomial function f(x) = x^3 - 12x^2 + 46x - 52. Participants suggest using the rational root theorem to list possible rational zeros and test x = 2 as a candidate. If x = 2 is confirmed as a root through synthetic division, the polynomial can be factored as (x - 2) times a quadratic polynomial. The remaining zeros can then be determined using polynomial long division and the quadratic formula. The conversation emphasizes systematic approaches to identifying both real and complex zeros of the polynomial.
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Polynomial function f(x)= x^3-12x^2+46x-52

A. List possible rational ZerosB. find all the zeros (real and complex) of the function (test x=2 as a rational zero using the synthetic division?
 
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shorty888 said:
A. List possible rational Zeros
Use the rational root theorem.

shorty888 said:
B. find all the zeros (real and complex) of the function (test x=2 as a rational zero using the synthetic division?
If x = 2 is a root, then the polynomial is divisible by x - 2 by the polynomial remainder theorem. You can use polynomial long division to find the ratio, which is a quadratic polynomial. Its roots can be found using the quadratic formula.
 
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