Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 5; zeros: 8, i, -8 iI have to enter the remaining zeros of f. I am a little...

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree 5; zeros: 8, i, -8 i

I have to enter the remaining zeros of f. I am a little bit confused on this question.

 

Asked on by amber756

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lemjay | High School Teacher | (Level 3) Senior Educator

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Zeros of a function y=f(x) refer to the values of x when y is zero. The number of zeros is equal to the degree of the function. Also, zeros of a function is also called as roots.

The given degree is 5. Then, there must be 5 values of x when y is zero.

Since there are three given zeros which are 8, i , and -8i, two values of x must be determined to complete the number of zeroes.

To do so, consider the given values i and -8i. These are complex numbers. Take note that if the roots are complex numbers they always come in pairs. And these pairs are always conjugate of each other in order for the coefficients of a polynomial function to be real numbers.

So, take the conjugate of `i` and  `-8i` .

> Conjugate of `i` : `-i`

> Conjugate of `-8i` :` 8i`

Hence, the other zeros of the function are `-i` and `8i` .

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