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

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

Step 1

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

$x^{7} \to 7$

$- x^{2} \to 2$

$1 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$7$

Step 3

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

$7$

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