Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6 will have

Question

five roots
three roots
Eight roots
Six roots

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots, counting multiplicity.

In the case of the polynomial y=8x^5−2x^4+6, the degree of the polynomial is 5, which means it will have exactly 5 roots, counting multiplicities.

Therefore, the correct answer is: Five roots.