9514 1404 393
Answer:
f(x) = x³ -7x² +17x -15
Explanation:
A polynomial with real coefficients will have complex roots in conjugate pairs. This means the third root is 2+i.
(x -p) is a factor when p is a zero
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The factorization is ...
f(x) = (x -3)(x -(2-i))(x -(2+i)) . . . . . zeros of 3, 2-i, 2+i
Expanding this to standard form gives ...
f(x) = (x -3)((x -2)² -i²) = (x -3)(x² -4x +4 +1)
f(x) = x(x² -4x +5) -3(x² -4x +5) = x³ -4x² +5x -3x² +12x -15
f(x) = x³ -7x² +17x -15