5.6 Find The Rational Zeros

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Presentation transcript:

5.6 Find The Rational Zeros Zeros is another word for solutions.

List Possible Rational Zeros Use p/q to find the possible rational zeros. p represents the factors of the constant term q represents the factors of the leading coeff. (EX) x3 + 2x2 – 11x + 12 p = factors of 12 (constant term) q = factors of 1 (leading coefficient) Make a list of all the possible combinations of p/q.

List the possible zeros of the polynomial below: (EX) f(x) = 4x4 – x3 – 3x2 + 9x – 10 (EX) f(x) = x3 + 9x2 + 23x + 15 (EX) f(x) = 2x3 + 3x2 – 11x – 6

Find zeros when the leading coefficient is 1. Step 1: List the possible rational zeros. p/q Step 2: Test the zeros using synthetic division. Use the possible factors as the substitution number until you get a remainder of 0. Step 3: Factor the trinomial and solve for x.

Find the zeros: (EX) f(x) = x3 – 8x2 + 11x + 20

Find zeros when the leading coefficient is not 1. (EX) f(x) = 10x4 – 11x3 – 42x2 + 7x + 12 Step1: List the possible p/q Step2: Choose reasonable numbers by viewing the graph. Step3: Check the reasonable numbers using synthetic division Step4: Factor the polynomial. Step5: Repeat the steps above with the new polynomial

Practice Problem: Find the zeros of the function: (EX) 2x4 + 5x3 – 18x2 – 19x + 42

CW/HW Page 374 (3,5,7,11,13,24)