# How many zeros does the function f(x) = 7x^{13} - 12x^{9} + 16x^{5} - 23x + 42 have?

**Solution:**

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

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

Given, the polynomial is 7x^{13} - 12x^{9} + 16x^{5} - 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) = 7x^{13} - 12x^{9} + 16x^{5} - 23x + 42 have?

**Summary:**

The function f(x) = 7x^{13} - 12x^{9} + 16x^{5} - 23x + 42 will have 13 zeroes. The degree of the given polynomial means the highest power of the polynomial.

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