Find the Maximum Number of Real Roots x^5+7x^4+2x^3+14x^2+x+7

$x^{5} + 7 x^{4} + 2 x^{3} + 14 x^{2} + x + 7$

Step 1

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

$x^{5} \to 5$

$7 x^{4} \to 4$

$2 x^{3} \to 3$

$14 x^{2} \to 2$

$x \to 1$

$7 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$5$

Step 3

The maximum number of possible roots is the degree of $x^{5} + 7 x^{4} + 2 x^{3} + 14 x^{2} + x + 7$ .

$5$