Smallest polynomial with given roots
Let be a monic polynomial with real coefficients such that and are both roots of Suppose that has the smallest possible degree given these requirements. What is
Clarification : .
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1 solution
Relevant wiki: Complex Conjugate Root Theorem
As 1 + i is a root, so does 1 − i (refer to the wiki above)
f ( x ) = ( x − 2 ) ( x − ( 1 + i ) ) ( x − ( 1 − i ) ) = x 3 − 4 x 2 + 6 x − 4
f ( 3 ) = 5