If a is a root of P(x)=0, then (x-a) is a factor of P(x). If P(x) is a polynomial with real coefficients, then the complex roots of P(x)=0 occur in conjugate pairs.
If P(x) is a polynomial with real coefficients, then the complex roots of P(x)=0 occur in conjugate pairs.
This theorem states that if a + bi is a complex root, then a- bi is also a root. Additionally, recall that if a is a root of P(x)=0, then (x-a) is a factor of P(x).
Root
Factor
5i
x-5i
-5i
x-(- 5i)
- 3
x-(-3)
Polynomial
P(x)= (x-5i) (x-(-5i)) (x-(-3))
Let's simplify the polynomial by applying the Distributive Property. For simplicity, we will start by multiplying the first two factors together, and then multiply this product by the last factor.
