Given the polynomial function \(f(x) = 2x^5 - 3x^4 + 5x^3 - 2x^2 + 3x - 5\), how many real roots/zeros can this function have at maximum?
Answer
Therefore, according to the Fundamental Theorem of Algebra, a polynomial of degree \(n\) has at most \(n\) real roots. So, this polynomial has at most 5 real roots.
Step 1 ：In order to find the maximum number of real roots of a polynomial function, we have to look at the degree of the polynomial. The degree of a polynomial is the highest power of the variable in the polynomial.
Step 2 ：In this case, the degree of the polynomial \(f(x) = 2x^5 - 3x^4 + 5x^3 - 2x^2 + 3x - 5\) is 5, as the highest power of \(x\) is 5.
Step 3 ：Therefore, according to the Fundamental Theorem of Algebra, a polynomial of degree \(n\) has at most \(n\) real roots. So, this polynomial has at most 5 real roots.
