How to Solve Quadratic Equations using the Quadratic Formula
The quadratic formula is a recipe for the roots of a quadratic equation. The roots describe if and where the curve becomes zero.
Other People Are Reading
Instructions
-
How to Solve a Quadratic Equation with the Quadratic Formula
-
1
Grab a quadratic equation, collecting terms of like powers in x. For example x^2 -6x+5 = 0. Here, the constant term is 5, the linear term is -6x and the quadratic term is x^2. From these, the constant coefficient is 5, the linear coefficient is -6 and the quadratic coefficient is 1.
-
2
Pull out the quadratic formula:(-b + sqrt(b^2-4ac)) / 2a & (-b - sqrt(b^2-4ac)) / 2aWithin the equation are multiple parts. (a,b,c) refers to the quadratic, linear and constant coefficients. For the example in step 1, (a,b,c) = (1,-6,5). sqrt() is the square root function.
-
-
3
Determine the properties of the roots. Look at the term within the square root. b^2-4ac compares to zero in one of three ways:b^2 - 4ac > 0 which means there are two real rootsb^2 - 4ac = 0 which means there is only one root.b^2 - 4ac > 0 which means there are two imaginary rootsIf your roots are imaginary, then one should stop here.In the example given, b^2-4ac = (-6)^2-4*5*1 = 36 - 20 = 16 > 0, which means I have two real roots
-
4
Solve for the roots. Plug in the values of the coefficients into the equation. In the given case(-b + sqrt(b^2-4ac))/2a = (6 + sqrt(16))/2 = 10/2 = 5,(-b - sqrt(b^2-4ac))/2a = (6 - sqrt(16))/2 = 2/2 = 1.The roots are then 1 and 5.
-
5
Use the roots to factor the original equation. The example provided is x^2-6x+5 = 0. Using the roots, this factors as (x-1)(x-5)=0.
-
1
