Math Problem Statement

A polynomial f(x) and one or more of its zeros are given. f(x) = x^4 -2x^3 +23x^2 +6x -78. 1=5i is a zero. a. FInd all zeros. Write the answer in exact form. If there is more than one answer, separate them with a comma

Solution

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Math Problem Analysis

Mathematical Concepts

Polynomial Equations
Complex Numbers
Quadratic Equations
Synthetic Division

Formulas

(x - r)(x - conjugate) = (x - r)^2 + imag(r)^2
Synthetic Division of Polynomials

Theorems

Complex Conjugate Theorem
Difference of Squares Theorem

Suitable Grade Level

Grades 10-12