Since the discriminant is 0, there is 1 real solution to the equation. 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 There are different methods you can use to solve quadratic equations, depending on your particular problem. 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. ( 1 2 b a ) 2 = b 2 4 a 2 ( 1 2 b a ) 2 = b 2 4 a 2 When there is no linear term in the equation, another method of solving a quadratic equation is by using the square root property, in which we isolate the (x2) term and take the square root of the number on the other side of the equals sign.
In this section we will derive and use a formula to find the solution of a quadratic equation. Not all quadratic equations can be factored or can be solved in their original form using the square root property. The first step, like before, is to isolate the term that has the variable squared. Notice that the quadratic term, x, in the original form ax 2 k is replaced with (x h). We can use the Square Root Property to solve an equation of the form a(x h) 2 k as well. Mathematicians look for patterns when they do things over and over in order to make their work easier. Solve Quadratic Equations of the Form a(x h) 2 k Using the Square Root Property. 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’.
When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Solve Quadratic Equations Using the Quadratic Formula