9
QuizMultiple Choice

Polynomial Functions and Theorems — Test

Question 9 • Algebra 2 with Probability

What is the polynomial function of lowest degree with leading coefficient 1 and roots 1 and 1 plus i ?

Answer
A
f of x is equal to x squared minus 2 x plus 2
B
f of x is equal to x squared minus x plus 2
C
f of x is equal to x cubed minus x squared plus 4 x minus 2
D
f of x is equal to x cubed minus 3 x squared plus 4 x minus 2

Explanation

For a polynomial with real coefficients, a non-real root 1 + i requires its conjugate 1 − i to be a root as well. The lowest-degree monic polynomial is therefore (x − 1)(x − (1 + i))(x − (1 − i)) = (x − 1)((x − 1)² + 1). Expanding gives x³ − 3x² + 4x − 2, which is choice A.

AI-written and checked against the verified answer.

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