Find the Maximum Number of Real Roots f(x)=x^5-2.1x^4-14.44x^3+3x^2+41.67x-15.216

$f (x) = x^{5} - 2.1 x^{4} - 14.44 x^{3} + 3 x^{2} + 41.67 x - 15.216$

Step 1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$x^{5} \to 5$

$- 2.1 x^{4} \to 4$

$- 14.44 x^{3} \to 3$

$3 x^{2} \to 2$

$41.67 x \to 1$

$- 15.216 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The maximum number of possible roots is the degree of $x^{5} - 2.1 x^{4} - 14.44 x^{3} + 3 x^{2} + 41.67 x - 15.216$ .

$5$