Find a polynomial function with real coefficients of degree 4 and zeros x=1-i and x=√(7). let the leading coefficient be equal to 1. written in factored form over rational numbers.

Step-by-step explanation:

Given that one of the zeroes is 1 - i.

Complex roots occur in pairs.

This means, if a + bi is a zero of a polynomial, then a - bi is also its zero.

Therefore, 1 + i is also a zero of the polynomial.

Factors are x - (1 - i) and x - (1 + i).

Multiply the factors.

[x - (1 - i)][x - (1 + i)] = (x - 1 + i)(x - 1 - i)

Given that one of the zeroes is .

Irrational roots occur in pairs.

This means, if an irrational number m is a zero of a polynomial, then - m is also its zero.

Therefore, is also a zero of the polynomial.

Factors are and .

Multiply the factors.

Hence, the required polynomial is .