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Precalculus PreAP/Dual, Revised Β©2017
Rational Zero Test Section 2.5 Precalculus PreAP/Dual, Revised Β©2017 11/3/ :34 AM Β§2.5: Rational Zero Test
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Finding Rational Zeros
Where the graphs cross the πβaxis (π is zero) Known as zeros or roots To find the realβnumber zeros, it can be rational, irrational and/or imaginary numbers To find out how many zeros the graph has, the easiest way to find the amount of degrees the graphs has 11/3/ :34 AM Β§2.5: Rational Zero Test
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Steps Identify the constant term and coefficient of the polynomial
List all multiples of each number and donβt forget the plus-or-minus symbol for each polynomial Apply the equation: π π = Factors of Constant Term Factors of Leading Coefficient List ALL of the possible rational zeros 11/3/ :34 AM Β§2.5: Rational Zero Test
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What multiplies with what equals that number?
Example 1 List all possible rational zeros for π π +ππ π π β ππ π +π=π What multiplies with what equals that number? 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 2 List all possible rational zeros for π π =π π π + π π βππ π π βππ+π 11/3/ :34 AM Β§2.5: Rational Zero Test
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Your Turn List all possible rational zeros for π π π βππ π π +ππ π π +πππβπ=π 11/3/ :34 AM Β§2.5: Rational Zero Test
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Steps Determine what the leading coefficient and constant term are.
Put it in the rational zero test π π Use synthetic division to find which factor gives the remainder of zero. If the polynomial cannot be factored, repeat steps 2 and 3 again Factor or use the Quadratic Formula to get the leftover polynomial out. Equal it all to zero and put it in π= form. 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 3 Find the real and imaginary rational zeros for π π = π π + π π βππβπ Step 1: What are the factors of the constant term and the leading coefficient? Constant Term (the number without the letter): Coefficient: (the number in front of the letter with the highest degree) Step 2: Put it in rationalβzero test 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 3 Find the real and imaginary rational zeros for π π = π π + π π βππβπ Step 3: Test each possible rational form 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 3 Find the real and imaginary rational zeros for π π = π π + π π βππβπ Step 4: Factor or use the Quadratic Formula to get the leftover polynomial out. 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 3 Find the real and imaginary rational zeros for π π = π π + π π βππβπ Step 5: Equal it all to zero and put it in π= form. 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 3 Find the real and imaginary rational zeros for π π = π π + π π βππβπ Step 6: Use graphing calculator to check 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 4 Find the real and imaginary rational zeros for π π =π π π +π π π βπππβπ 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 5 Find the real and imaginary rational zeros for π π = π π βπ π π +πππβπ 11/3/ :34 AM Β§2.5: Rational Zero Test
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Your Turn Find the real and imaginary rational zeros for π π =π π π + π π βπππ+π 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 1: What are the factors of the constant term and the leading coefficient? Step 2: Apply p/q 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 3: Test each possible rational form 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 3: Test each possible rational form 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 4: Identify the equation & Solve 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 4: Identify the equation & Solve 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 6 Find the real and imaginary rational zeros for π π =π π π + π π βππ π π βππ+π Step 5: Check 11/3/ :34 AM Β§2.5: Rational Zero Test
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Example 7 Find the real and imaginary rational zeros for π π = π π β π π β π π βπβπ 11/3/ :34 AM Β§2.5: Rational Zero Test
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Assignment Worksheet 11/3/ :34 AM Β§2.5: Rational Zero Test
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