Quadratic Equations
A quadratic equation is one that can be put in the form ax2 + bx + c = 0 where a, b, and c are numbers and a is not zero (b and/or c might be zero).
For instance
3x2 + 7x = 4 is a quadratic equation.
3x2 + 7x = 4
– 4 –4
3x2 + 7x – 4 = 0
In this
example a ¼ 3, b ¼ 7, and c ¼ _4.
There are two main approaches to solving
these equations. One approach uses the fact that if the product of two numbers
is zero, at least one of the numbers must be zero. In other words, wz = 0
implies w = 0 or z ¼ 0 (or both w ¼ 0 and z = 0.) To use this fact on a
quadratic equation first make sure that one side of the equation is zero and
factor the other side. Set each factor equal to zero then solve for x.
Examples
x2
+ 2x – 3 = 0
x2
+ 2x – 3 can be factored as (x + 3)(x – 1)
x2
+ 2x – 3 ¼ 0 becomes (x + 3)(x – 1) = 0
Now set each
factor equal to zero and solve for x.
You can
check your solutions by substituting them into the original equation.
3x2
– 9x – 30 = 0 becomes 3(x2 – 3x – 10) = 0 which becomes 3(x – 5) (x +
2) = 0.
The factor 3
was not set equal to zero because ‘‘3 = 0’’ does not lead to any solution.
Practice
Solutions
“Sumber Informasi”
Thanks for reading Quadratic Equations. Please share...!
