Question

How many zeros does the function f(x) = 7x13 − 12x9 + 16x5 − 23x + 42 have?

Answer 1

According to the fundamental theorem of algebra, the number of solutions (or zeroes) of an equation equals the value of the highest termed exponent.
In this case it is 13.

Answer 2

The given polynomial will have 13 zeroes.

Explanation:

We have been given a polynomial

`f(x)=7x^(13)-12x^9+16x^5-23x+42`

Since, the degree of given polynomial means the highest power of the polynomial which is 13 here in given polynomial

By fundamental theroem of algebra which says that the number of zeroes is equal to the degree of polynomial.

Since, degree of given polynomial is 13

Therefore given polynomial will have 13 zeroes.