Patricia is studying a polynomial function f (x). Three given roots of f (x) are - 11-square root 2i, 3 + 4i, and 10. Patricia concludes that f (x) must be a polynomial with degree 4. Which statement is true?

Question

Taylor Hendricks

Mathematics

7 November, 00:22

Patricia is studying a polynomial function f (x). Three given roots of f (x) are - 11-square root 2i, 3 + 4i, and 10. Patricia concludes that f (x) must be a polynomial with degree 4. Which statement is true?

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Answers (2)

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Marie Blankenship · Answer 1

its D on edge

Luna Wiley · Answer 2

In order for the polynomial to be a degree of 4, it must have exactly 4 roots. According to the fundamental theorem of algebra: "The number of roots in a function is equivalent to the degree of the function"

These roots do not have to be real numbers, which means they can be imaginary or complex.

In this case, (-11 - √2i), (3 + 4i), and 10. There are three roots, which means that the polynomial can be a third of fourth degree polynomial. It is wrong for Patricia to assume that this is a fourth degree polynomial when only three roots are known.

The degree of the polynomial will at least be three, but could be higher.