Find the Maximum Number of Real Roots f(x)=4x^3-13x^2+9x+2

$f (x) = 4 x^{3} - 13 x^{2} + 9 x + 2$

Step 1

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

$4 x^{3} \to 3$

$- 13 x^{2} \to 2$

$9 x \to 1$

$2 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$3$

Step 3

The maximum number of possible roots is the degree of $4 x^{3} - 13 x^{2} + 9 x + 2$ .

$3$