The discussion focuses on finding all zeros of the polynomial function f(x) = x^3 - 12x^2 + 46x - 52. The Rational Root Theorem is employed to list possible rational zeros, with x = 2 tested as a candidate using synthetic division. Confirming that x = 2 is a root allows for the polynomial to be factored as (x - 2)(quadratic polynomial). The remaining zeros are determined using the quadratic formula on the resulting quadratic polynomial.
PREREQUISITESStudents and educators in mathematics, particularly those studying algebra and polynomial functions, as well as anyone involved in solving equations and finding roots of polynomials.
Use the rational root theorem.shorty888 said:A. List possible rational Zeros
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.shorty888 said:B. find all the zeros (real and complex) of the function (test x=2 as a rational zero using the synthetic division?