Find the Maximum Number of Real Roots f(x)=-3x^4+7x^3+3x^2-9x-1

$f (x) = - 3 x^{4} + 7 x^{3} + 3 x^{2} - 9 x - 1$

Step 1

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

$- 3 x^{4} \to 4$

$7 x^{3} \to 3$

$3 x^{2} \to 2$

$- 9 x \to 1$

$- 1 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Step 3

The maximum number of possible roots is the degree of $- 3 x^{4} + 7 x^{3} + 3 x^{2} - 9 x - 1$ .

$4$