Homework Clinic

Mathematics Clinic => Grade 10 Mathematics => Topic started by: j_sun on Jun 17, 2013

Title: how do you find the roots of a quadratic?
Post by: j_sun 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 (:

Title: how do you find the roots of a quadratic?
Post by: camila 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").

Title: how do you find the roots of a quadratic?
Post by: ricki 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.