Question

If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is _.

Answer 1

Answer: If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.

Step-by-step explanation:

• We know that when a complex number $z=a+ib$ is a root of a polynomial with degree 'n' , then the conjugate of the complex number ($\overline{z}=a-ib$) is also a root of the same polynomial.

Given: 7+5i is a zero of a polynomial function of degree 5 with coefficients

Here, 7+5i is a complex number.

So, it conjugate ($\overline{7+5i}=7-5i$) is also a zero of a polynomial function.

Hence, if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.