The process of determining the equation given its roots hinges on the understanding that the sum and product of the roots have a certain relationship with the equation's coefficients. In the context of quadratic equations, if the roots are identified as 'a' and 'b', then the equation can be represented as x²-(a+b)x+ab=0. For cubic equations, the method follows a similar pattern, albeit with a greater number of coefficients involved.
| Topic | Problem | Solution |
|---|---|---|
| None | Find the equation of a polynomial given the roots… | Given the roots, we can express the polynomial as \((x - 2)(x + 3)(x - 1)\). |