Final answer:
The two linear factors of a quadratic equation with zeros b and -c are (x - b) and (x + c). These factors, when equated to zero, give the solutions of the quadratic equation, which can be determined using the quadratic formula.
Step-by-step explanation:
If the zeros of a quadratic equation are b and -c, this means that the solutions to the equation are the values that would make the equation zero when substituted for the variable. Since the roots or solutions of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula, the two linear factors of the equation would be (x - b) and (x + c), because these factors correspond to the zeros of the equation. To solve a quadratic equation, you would set each factor equal to zero and solve for x, getting the solutions b and -c respectively.
For example, if we have a quadratic equation with a constant a = 1.00, and its solutions are given by the quadratic formula, and the suppose zeros are 2 and -3, then the linear factors would be (x - 2) and (x + 3). When multiplied together, these two linear factors will give you the quadratic equation x² - x - 6 which has 2 and -3 as its solutions. The linear factors are the simplest form of the polynomial that will be zero at the roots of the quadratic equation.