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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.
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