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

Solution:

For any polynomial expression, the zeroes are those values of the variable for which the polynomial as a whole has zero value.

Since we are restricted to the set of Reals, we will always consider zeroes which have real values. 

Given, the polynomial is 7x¹³ - 12x⁹ + 16x⁵ - 23x + 42

The degree of the given polynomial means the highest power of the polynomial.

Here,

degree of the polynomial is 13.

By fundamental theorem of algebra,

Number of zeroes = degree of polynomial

Number of zeroes = 13

Therefore, the given function will have 13 zeroes.

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

Summary:

The function f(x) = 7x¹³ - 12x⁹ + 16x⁵ - 23x + 42 will have 13 zeroes. The degree of the given polynomial means the highest power of the polynomial.