MHF4U
2.9 SOLVING POLYNOMIAL EQUATIONS
The real roots of polynomial equation 𝑃(𝑥) = 0 correspond to the x-intercepts of the graph of
the polynomial function 𝑃(𝑥).
If a polynomial equation is factorable, the roots are determined by factoring the polynomial,
setting its factors equal to zero, and solving each factor.
If a polynomial equation is not factorable, the roots can be determined from the graph using
technology or quadratic formula (
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
) for the 2nd degree polynomial .
Example 1
Determine the real roots of each polynomial:
a) (2𝑥 2 + 8)(𝑥 2 − 25) = 0
b) (2𝑥 − 5)(1 − 3𝑥)(𝑥 − 1.5) = 0
Example 2
Solve polynomial by factoring:
a) 𝑥 3 − 𝑥 2 − 2𝑥 = 0
b) 𝑥 3 − 𝑥 2 − 9𝑥 + 9 = 0
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Example 3
Solve each of the following:
a) 𝑥 3 + 9𝑥 2 + 13𝑥 + 5 = 0
b) 𝑥 3 − 2𝑥 − 4 = 0
Practice/Homework: pg. 110-111 # 1a,e,3a,c,e,4a,c,e,6a,b,7a,b,8,b,d,10,11
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