How many zeros does the function f (x) = 3x12 - 17x8 + 11x4 - 6x + 23 have?

How many zeros does the function f (x) = 3x12 - 17x8 + 11x4 - 6x + 23 have?

Answer: the third option (12 zeroes ...).

Use ^ to denote an exponent ...

f (x) = 3x^12 - 17x^8 + 11x^4 - 6x + 23 ...

We know from that fact that the number of zeroes (real or complex) in a polynomial is the same as the degree of the polynomial ...

The degree is the greatest/highest power of the terms, which in this case is 12 (since 12 is the greatest exponent ...) ...

The degree is 12, thus it means there are 12 zeroes ...

Answer: the third option (12 zeroes) ...