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

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21-10-2021
Mathematics

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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

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joaobezerra joaobezerra · Answer 1 · 2021-10-29T11:59:39+02:00

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 [tex]a + bi[/tex], and it's conjugate is [tex]a - bi[/tex].

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 https://brainly.com/question/24450834