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

Answer:

The function has 23 zeros.

Step-by-step 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.