Math Tutoring on Finding the Zeros of Polynomial Functions
Let us find the connections among the real rational zeros, the factors and the graphs of polynomial functions.
and c is a real number such that f(c) = 0. So if we substitute the value of c into the function, the function value is zero. So we say,
1. The real number c is a zero or root of the polynomial function f(x).
2. x = c is a solution to the equation f(x) = 0.
3. The quantity (x – c) is a factor of the polynomial function f(x).
4. The point (c, 0) is an x intercept of the graph of the polynomial function f(x).
Also a polynomial function of degree n with complex coefficients in the form
has exactly n complex zeros, counting multiplicity. This is the Complex Factorization Theorem.
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1. What are the zeros of a polynomial function?
2. `What are the zeros of a polynomial?
3. What is a simple zero?
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