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hodyreva [135]
3 years ago
11

How many total roots must there be in this fourth-degree function?

Mathematics
1 answer:
Anna71 [15]3 years ago
6 0

Answer:

<em>It must have 4 roots</em>

Step-by-step explanation:

<u>Fundamental Theorem of Algebra</u>

One polynomial of degree n will have exactly n roots. The degree of a polynomial is the highest exponent of its variable. Some of the roots could be real, some could be imaginary (complex). If n is odd, at least one of the roots is real.

The polynomial given in the question is

H(x)=4x^{4} -5x^{3}+2x^{2}-x+5

has a degree of 4 (the highest exponent of x). According to the Fundamental Theorem of Algebra, it must have 4 roots

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