Solving a quadratic equation by factoring 1

quadratic equation, factoring, solving equations

There are three common ways to solve quadratic equations. The first method one should try is by factoring.  

Quadratic equations are second degree equations and they have two roots, also known as solutions.  These solutions may be real or imaginary.  When the roots are real, they may be either two distinct solutions or the same, also known as double roots.  It is important to list both roots as solutions even if they are the doulbe roots.

Example:

Solve for y:

y² +5y + 6 = 0

This expression can be factored into

(y+2)(y+3) = 0

We set both of these factors equal to 0:

(y+2) = 0
(y+3) = 0

y+2 = 0
  –2   –2
y = -2

Similarly, y = -3

These results in two values for y, -2 and -3.

The solution to the above expression would be y = -2, -3 or y = -2 and y = -3

Here is another example.

y² - 6y + 9 = 0

The expression on the left side may be factored as follows:

(y-3)(y-3) = 0

This may also be written as (y-3)².

To solve, set each binomial in parentheses equal to 0:

y-3=0
+3 +3

y=3

This applies to both expressions in parentheses.

The answer is y= -3, -3 or y= -3 and y= -3.

It is important that the double root be noted in your answer.

quadratic equation, factoring, solving equations