Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 0,1, and 1+i

Step-by-step explanation:

The standard polynomial is given by:

Where a is the leading coefficient and p and q are the zeros.

We are given that the zeros are x = 0, 1, and 1 + i.

First, by the Complex Root Theorem, if 1 + i is a zero, then 1 - i must also be a zero.

Therefore:

Simplify:

Expand the third and fourth factors:

Distribute:

Expand:

Therefore:

Hence, our polynomial function is:

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x