How many zeros does the function f(x) = 2x¹⁴ - 14x⁶ + 27x³ - 13x + 12 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:

2x¹⁴ - 14x⁶ + 27x³ - 13x + 12

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

Here, the degree of the polynomial is 14.

By fundamental theorem of algebra,

Number of zeroes = degree of polynomial

Number of zeroes = 14

Therefore, the given function will have 14 zeroes.

How many zeros does the function f(x) = 2x¹⁴ - 14x⁶ + 27x³ - 13x + 12 have?

Summary:

The function f(x) = 2x¹⁴ - 14x⁶ + 27x³ - 13x + 12 will have 14 zeroes. The degree of the given polynomial means the highest power of the polynomial.