(ax2 + bx + c 0) Factor the quadratic expression. Often, the simplest way to solve 'ax 2 + bx + c 0' for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. Set the equation equal to zero, that is, get all the nonzero terms on one side of the equal sign and 0 on the other. You can use the Quadratic Formula any time youre trying to solve a quadratic equation as long as that equation is in the form '(a quadratic expression) that is set equal to zero'. Since the discriminant is 0, there is 1 real solution to the equation. To solve quadratic equations by factoring, we must make use of the zero-factor property. Since the discriminant is negative, there are 2 complex solutions to the equation.Ī = 9, b = −6, c = 1 a = 9, b = −6, c = 1 Since the discriminant is positive, there are 2 real solutions to the equation.Ī = 5, b = 1, c = 4 a = 5, b = 1, c = 4 The equation is in standard form, identify a, b, and c.Ī = 3, b = 7, c = −9 a = 3, b = 7, c = −9 To determine the number of solutions of each quadratic equation, we will look at its discriminant. The left side is a perfect square, factor it.Īdd − b 2 a − b 2 a to both sides of the equation.ĭetermine the number of solutions to each quadratic equation.
By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’.
Although the quadratic formula works on any quadratic equation in standard form, it is easy to make errors in substituting the values into the formula.
When we solved quadratic equations in the last section by completing the square, we took the same steps every time. The fourth method of solving a quadratic equation is by using the quadratic formula, a formula that will solve all quadratic equations. Solve Quadratic Equations Using the Quadratic Formula It is based on a right triangle, and states the relationship among the lengths of the sides as \(a^2+b^2=c^2\), where \(a\) and \(b\) refer to the legs of a right triangle adjacent to the \(90°\) angle, and \(c\) refers to the hypotenuse.\) One of the most famous formulas in mathematics is the Pythagorean Theorem.