SOLUTION: How do I find the polynomial p(x) with real coefficients of the smallest degree that satisfies the given conditions: p(x) has zeros at x=0, 1/2, 1+ i, and p(1)=2.

Question 736102: How do I find the polynomial p(x) with real coefficients of the smallest degree that satisfies the given conditions: p(x) has zeros at x=0, 1/2, 1+ i, and p(1)=2.
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
Start with focusing on the zeros. The complex with imaginary part needs also its conjugate. Your simplest function is
=.

When you let x=1, you find that the expression evaluation results in value of 1/2. You want p(1)=2, which is an increase by a factor of 4, so you want
and you could fully multiply the expression into the polynomial if you want it in general form.
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