According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f of x is equal to 4 x to the 5th power minus 3 x

The Fundamental Theorem of Algebra says a polynomial of degree n has exactly n roots when complex roots are counted with multiplicity. The polynomial 4x^5 − 3x has degree 5, so it has 5 roots. Therefore, the correct choice is “5 roots.”

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