# ### Author Question: how do you find the roots of a quadratic? (Read 1749 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").

### Need homework help now?

#### 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.

Did you know?

Many medications that are used to treat infertility are injected subcutaneously. This is easy to do using the anterior abdomen as the site of injection but avoiding the area directly around the belly button.

Did you know?

Giardia is one of the most common intestinal parasites worldwide, and infects up to 20% of the world population, mostly in poorer countries with inadequate sanitation. Infections are most common in children, though chronic Giardia is more common in adults.

Did you know?

Nearly all drugs pass into human breast milk. How often a drug is taken influences the amount of drug that will pass into the milk. Medications taken 30 to 60 minutes before breastfeeding are likely to be at peak blood levels when the baby is nursing.

Did you know?

Not getting enough sleep can greatly weaken the immune system. Lack of sleep makes you more likely to catch a cold, or more difficult to fight off an infection.

Did you know?

The horizontal fraction bar was introduced by the Arabs.

For a complete list of videos, visit our video library