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

[shorty888]

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?

 

[Evgeny.Makarov]

A. List possible rational Zeros

Use the rational root theorem.

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.