Final answer:
The student needs to find the roots of the polynomial f(x) = x⁴ - 56x³ + 1070x² - 8200x + 20600. Typically, for quadratic equations, the quadratic formula is used after arranging the equation into standard form ax² + bx + c = 0. However, this fourth-degree polynomial may require numerical methods or computer algebra systems to solve.
Step-by-step explanation:
The student has asked to find the roots of the polynomial function f(x) = x⁴ - 56x³ + 1070x² - 8200x + 20600. To find the roots of a polynomial, we can either factor the polynomial directly, use synthetic division, or apply the Rational Root Theorem.
However, this polynomial is quite complex and traditional methods may be tedious or impractical. For such higher-degree polynomials, numerical methods or computer algebra systems might be necessary to find the exact roots.
For simpler cases, such as a quadratic equation, you can use the quadratic formula to find the roots.
The quadratic formula is given by x = (-b ± √(b²-4ac))/(2a) for an equation of the form ax² + bx + c = 0. You would first need to arrange your equation in this standard form before applying the formula.