Write a polynomial function with degree 3 with the given zeros x=1, x=3i

Answer 1

If 3i is a root, so is -3i.

If 3i is a root, then (x-3i) is a factor of the polynomial function.

If - 3i is a root, then (x-(-3i)) = (x+3i) is a factor.

If 1 is a root, then (x-1) is a factor.

So polynomial functions satisfying the given have the form:

f(x) = A(x-3i)(x+3i)(x-1), where A is nonzero number.

The product (x-3i)(x+3i) results in a difference of squares, x²-(3i)²=x²-9i²=x²+9

The product (x²+9)(x-1) = x³-x²+9x-9.

Your choice as to the value of A: A(x³-x²+9x-9)

Use the slider on A for this graph and notice that the root x= 1 remains in place.

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