Question

According to the fundamental theorem of algebra, how many zeros does the function f(x) = 15x23 + 41x19 + 13x5− 10 have?

3
5
19
23

Answer 1

The solutions to an algebraic equation equal the highest power in that equation. So, in this case, the answer is 23.

Answer 2

The function has 23 zeros.

Explanation:

Fundamental Theorem of Algebra-

Any polynomial of degree n has n roots or zeros.

The given function is,

`f(x) = 15x^(23) + 41x^(19) + 13x^5- 10`

In the polynomial
`15x^(23) + 41x^(19) + 13x^5- 10`, the highest power is 23.

So, according to fundamental theorem of algebra, there must be 23 roots or zeros of this polynomial.