Question

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

Answer 1

The function f(x) has 14 zeros.

Explanation:

We know that by Fundamental Theorem of Algebra :

Any polynomial equation of degree n with complex coefficient has exactly 'n' complex roots counting multiplicity.

Here we are given a polynomial function f(x) as:

`f(x)=2x^(14)-14x^6+27x^3-13x+12`

So, this polynomial function is of degree 14.

Hence, the given polynomial function f(x) has exactly 14 zeros.

Answer 2

14 zeros

Explanation:

For functions, the highest power is the amount of zeros. The highest power in this equation is 14 so it has 14 zeros.