Presentation on theme: "Bellwork Write the equation of the graph below in factored form."— Presentation transcript:
1 BellworkWrite the equation of the graph below in factored form.
2 Bell work Identify the type of polynomial Identify the number of solutionsIdentify the type of solutions (Classify)
3 7.5 Zeros of Polynomial Functions Students will be able to:Use the Rational Root Theorem and the Complex Conjugate Root Theorem to find the zeros of a polynomial function.Use the Fundamental Theorem to write a polynomial function given sufficient information about its zeros.
4 Rules and Properties Complex Conjugate Theorem 7.5 Zeros of Polynomial FunctionsRules and PropertiesComplex Conjugate TheoremIf P is a polynomial function with real-number coefficientsand a + bi is a root (zero).then a – bi is also a root (zero).
5 Rules and Properties Rational Root Theorem 7.5 Zeros of Polynomial FunctionsRules and PropertiesRational Root TheoremP is a polynomial function with integer coefficients.If is a root of P(x) = 0, thenpqp is a factor of the constant term of P.q is a factor of the leading coefficient of P.
6 Example 1Using the Rational Root Theorem, list all the POSSIBLE roots of the polynomial below.
7 Problem 1Using the Rational Root Theorem, list all the POSSIBLE roots of each polynomial below.
8 Problem 3Find all roots to the polynomial equation below.
9 7.5 Zeros of Polynomial Functions Problem 2Write the equation for a third degree polynomial whose zeros are listed below and P(0) = -6 in factored & standard form.
10 7.5 Zeros of Polynomial Functions Example 2Write the equation for a third degree polynomial whose zeros are 2 and i and P(0) = 4 in both factored & standard form.
11 Problem 4According to the Fundamental Theorem of Algebra, what can I conclude about the polynomial below?2. Given -6 as a root of the polynomial above, find the remaining roots.
12 Homework7.5: P even, odd, 41-43all, 47 (graphing calculator, synthetic division and factoring. You must show work.Test Tuesday- We have a no calc portion.