Author Question: how do you find the roots of a quadratic? (Read 2095 times)

j_sun

  • Sr. Member
  • ****
  • Posts: 384
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").



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

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?

All patients with hyperparathyroidism will develop osteoporosis. The parathyroid glands maintain blood calcium within the normal range. All patients with this disease will continue to lose calcium from their bones every day, and there is no way to prevent the development of osteoporosis as a result.

Did you know?

The Food and Drug Administration has approved Risperdal, an adult antipsychotic drug, for the symptomatic treatment of irritability in children and adolescents with autism. The approval is the first for the use of a drug to treat behaviors associated with autism in children. These behaviors are included under the general heading of irritability and include aggression, deliberate self-injury, and temper tantrums.

Did you know?

During pregnancy, a woman is more likely to experience bleeding gums and nosebleeds caused by hormonal changes that increase blood flow to the mouth and nose.

Did you know?

Green tea is able to stop the scent of garlic or onion from causing bad breath.

Did you know?

Before a vaccine is licensed in the USA, the Food and Drug Administration (FDA) reviews it for safety and effectiveness. The CDC then reviews all studies again, as well as the American Academy of Pediatrics and the American Academy of Family Physicians. Every lot of vaccine is tested before administration to the public, and the FDA regularly inspects vaccine manufacturers' facilities.

For a complete list of videos, visit our video library