# ### Author Question: how do you find the roots of a quadratic? (Read 1957 times)

#### j_sun

• Sr. Member
•    • Posts: 384
on: Jun 17, 2013
i know how to find the vertex and axis of semetry, but idkk how to find the roots without graphing! please helppp (:

#### camila

• Hero Member
•     • Posts: 705
Reply #1 on: Jun 17, 2013
A root is also called the "zero."

Factor it out, set it equal to zero, ta-da!

Example:

y = x^2 + 6x + 8
y = (x + 4)(x + 2)

x + 4 = 0
x = -4

x + 2 = 0
x = -2

Plug it in to your long equation, it should equal 0:

y = (-2)^2 + 6(-2) + 8 = 4 - 12 + 8 = 0
y = (-4)^2 + 6(-4) + 8 = 16 - 24 + 8 = 0

Yay!

Edit:  Quadratics always have 2 roots, although some times they are the same number (a "double root").

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#### ricki

• Full Member
•   • Posts: 200
Reply #2 on: Jun 17, 2013
factoring is one method, but it is not always easy to come up with the factors.  Another is Completing the Square, which is a technique of manipulating the equation into an equivalent equation that is easier to find the roots of.  The Quadratic formula solves quadratics of the form:

ax^2 + bx + c = 0.  It is derived by completing the square on this equation resulting in:

x = (-b +/- (b^2 - 4ac)^.5)/2a

+/- means plus or minus
^.5 means to the 1/2 power (the square root)

try searching on "completing the square" to get a description of the technique.

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