Final answer:
The given polynomial is a fourth-degree polynomial. To solve for the roots, we can use the quadratic formula: x = (-b ± √(b²-4ac)) / (2a)
Step-by-step explanation:
The given polynomial is 9x⁴-2x³-1. This is a polynomial expression with four terms. The highest power of x is 4, so it is a fourth-degree polynomial. To solve for the roots or x-intercepts of the polynomial, we set it equal to zero and use factoring or the quadratic formula. However, in this case, factoring doesn't seem to work since the polynomial doesn't have any common factors. We can use the quadratic formula, which states that for any quadratic equation of the form ax²+bx+c=0, the solutions are given by:
x = (-b ± √(b²-4ac)) / (2a)