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Write A Polynomial function with real coefficient whose zeros and their multiplicities include those listed: Degree 3: zeros: 2-i, -1, f(2)=6
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Write A Polynomial function with real coefficient whose zeros and their multiplicities include those listed: Degree 3: zeros: 2-i, -1, f(2)=6
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Since 2 - i is a zero, its conjugate 2 + i must also be a zero. Thus
f(x) = (x - (2 - i))(x - (2 + i))(x + 1)
f(x) = ((x - 2) - i)((x - 2) + i)(x + 1)
f(x) = ((x - 2)^2 + 1)(x + 1)
f(x) = (x^2 - 4x + 4 + 1)(x + 1)
f(x) = (x^2 - 4x + 5)(x + 1)