Find a polynomial with integer coefficients that satisfies the given conditions.Q has degree 3, and zeros 0 and i.

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

Step 1: Identify the roots The roots are 0, i, and -i.

Step 2: Write the factors The factors of the polynomial are (x - 0), (x - i), and (x - (-i)).

Step 3: Simplify the factors Simplify the factors to get x, (x - i), and (x + i).

Step 4: Write the polynomial The polynomial Q(x) is the product of these factors. So, Q(x) = x(x - i)(x + i).

Step 5: Expand the polynomial Expand the polynomial to get Q(x) = x(x^2 + 1).

Step 6: Simplify the polynomial Simplify the polynomial to get Q(x) = x^3 + x.

So, the polynomial with integer coefficients that satisfies the given conditions is Q(x) = x^3 + x.