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

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

Step 1

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

$2 x^{4} \to 4$

$- 7 x^{3} \to 3$

$4 x^{2} \to 2$

$2 x \to 1$

$3 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$4$