Author Question: how do you find the roots of a quadratic? (Read 4999 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?

The most common childhood diseases include croup, chickenpox, ear infections, flu, pneumonia, ringworm, respiratory syncytial virus, scabies, head lice, and asthma.

Did you know?

Illicit drug use costs the United States approximately $181 billion every year.

Did you know?

Women are two-thirds more likely than men to develop irritable bowel syndrome. This may be attributable to hormonal changes related to their menstrual cycles.

Did you know?

The human body's pharmacokinetics are quite varied. Our hair holds onto drugs longer than our urine, blood, or saliva. For example, alcohol can be detected in the hair for up to 90 days after it was consumed. The same is true for marijuana, cocaine, ecstasy, heroin, methamphetamine, and nicotine.

Did you know?

There are actually 60 minerals, 16 vitamins, 12 essential amino acids, and three essential fatty acids that your body needs every day.

For a complete list of videos, visit our video library