rational root and complex conjugates theorem. rational root theorem used to find possible rational...
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Rational Root and Complex Conjugates Theorem
Rational Root Theorem
• Used to find possible rational roots (solutions) to a polynomial
• Possible Roots : P/Q
• Where P represents the factors of the constant of the polynomial and Q represents the factors of the leading coefficient
Rational Root Theorem
2
9,9,
2
3,3,
2
1,1
2
9,
1
9,
2
3,
1
3,
2
1,
1
1:
2,1:
9,3,1:
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q
p
q
p
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Rational Root Theorem
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Rational Root Theorem
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Complex Conjugates Theorem
• If a + bi is a zero of the polynomial, then a – bi is a zero also.
• Ex. Find the polynomial whose zeros include 3 and 2 – i
Find the lowest degree polynomial with the following roots
i 6,5,3
Find the lowest degree polynomial with the following roots
i
oftymultipliciawith
21
22
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