Find the Maximum Number of Real Roots f(x)=ax^5+bx^3+cx-1

$f (x) = a x^{5} + b x^{3} + c x - 1$

Step 1

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

$a x^{5} \to 6$

$b x^{3} \to 4$

$c x \to 2$

$- 1 \to 0$

Step 2

The largest exponent is the degree of the polynomial.

$6$

Step 3

The maximum number of possible roots is the degree of $a x^{5} + b x^{3} + c x - 1$ .

$6$