Find the polynomial of least degree in standard form with the given roots:
x = 2, 3i
1 answer:
Answer:
x^3 - 2x^2 + 9x - 18.
Step-by-step explanation:
The complex roots occur in conjugate pairs so there are 3 roots 2, 3i and -3i.
So we have:
P(x) = (x - 2)(x - 3i)(x + 3i)
= (x - 2)(x^2 - 9i^2)
= (x - 2)(x^2 - 9*-1)
= (x - 2)(x^2 + 9)
= x^3 + 9x - 2x^2 - 18
= x^3 - 2x^2 + 9x - 18.
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