Solving Quadratic Equations
Equations such as x
2
= 64, x
2
-5x = 0, and x
2
+ 4x = 5 are called quadratic equations.
This
is because in each of these equations the greatest exponent of any variable is 2.
Standard Form of Quadratic Equations
:
ax
2
+ bx + c = 0
Before you select the method that you will use to solve a quadratic, you must use inverse
operations to get the equation to equal
zero
(if necessary).
When solving quadratic equations, we can use two methods:
1)
Factoring
2)Quadratic FormulaSolving Quadratic Equations Using Factoring:To Solve a Quadratic Using Factoring:1)Put the quadratic equation into standard form (above).2)Factor the quadratic expression.3)Set each factor equal to zero.4)Solve each equation.5)Check each root in the original equation.For example:x2+ 4x = 5-5 -5x2+ 4x – 5 = 0(x + 5)(x – 1) = 0x + 5 = 0 x – 1 = 0-5 -5 +1 x = -5 or x = 1Now, check in the original!!!Solve each quadratic equation using factoring:
+1