Find a polynomial with integer coefficients that satisfies the given conditions.P has degree 3 and zeros 5 and i.

To find a polynomial with integer coefficients that satisfies the given conditions, we need to remember that complex roots always come in conjugate pairs. This means that if "i" is a root, then "-i" is also a root.

Step 1: Write down the roots The roots are 5, i, and -i.

Step 2: Write down the factors The factors of the polynomial are (x-5), (x-i), and (x+i).

Step 3: Multiply the factors We multiply the factors to get the polynomial.

First, multiply the complex factors: (x - i)(x + i) = x^2 - i^2 = x^2 - (-1) = x^2 + 1

Then, multiply this result by the remaining factor: (x - 5)(x^2 + 1) = x^3 - 5x^2 + x - 5

So, the polynomial with degree 3 and zeros 5, i, and -i is P(x) = x^3 - 5x^2 + x - 5.