What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?
2 answers:
Answer:
f(x) = x3 – 3x2 + 4x – 2
Step-by-step explanation:
x³ - 3x² + 4x - 2
complex roots occur in conjugate pairs
1 + i is a root then so is 1 - i
the factors of the polynomial are therefore
f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))
= (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )
= x³ - 3x² + 4x - 2
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