The sum of the two roots of a quadratic equation is and their product is . Which of the following could be the equation?
Select an Answer
One way to do this problem is to think about the properties of roots. Suppose the two roots of a quadratic equation are and . Then the quadratic equation can be written in factored form as . The sum of the roots is , and the product is .
Note that. In this question the sum of the roots is and the product is . Therefore, and . The equation could be , which is choice B. Note that the roots of this equation are and . Their sum is and their product is .
If you know these properties of roots, you do not need to factor all of the equations to find the one that fits the given conditions.