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# How many zeros does the function f(x) = 2x^{14} - 14x^{6} + 27x^{3} - 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:

2x^{14} - 14x^{6} + 27x^{3} - 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) = 2x^{14} - 14x^{6} + 27x^{3} - 13x + 12 have?

**Summary:**

The function f(x) = 2x^{14} - 14x^{6} + 27x^{3} - 13x + 12 will have 14 zeroes. The degree of the given polynomial means the highest power of the polynomial.

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