Question

A polynomial function of degree 4 with real coefficients could have -3, 1+i, 1-i, and -3,7i as its zeros. true or false

Answer 1

Using complex numbers concepts, it is found that the statement is false.

When a complex number is a root of a polynomial function, it's conjugate also has to be.

• A complex number has the format $a + bi$, and it's conjugate is $a - bi$.

In this problem:

• Real root -3.
• Complex-conjugate roots 1 + i and 1 - i.
• Complex root -3 + 7i.

The conjugate of -3 + 7i also has to be a root, which would make the polynomial of the 5th degree, as it would have 5 roots, thus, the statement is false.

A similar problem is given at brainly.com/question/24450834