How do we solve quadratic equations?
What are quadratic equations for that matter?
Let's find out.
So a quadratic equation is an equation where the highest coefficient's variable is a square.
 |
| In this example, a is the highest variable because it's variable is squared. |
There are 2 best ways to solve a quadratic equation:
- Factoring the equation - when factoring you have to try to put the equation into two parts that can be multiplied and equal the equation. For example :
x² - 8x + 15
(*first find two numbers that multiply to 15, but add to -8*)
(x - 5) (x - 3)
(*you get -5 and -3, which both multiply to 15 and add to -8*)
So your answers would be 5 and 3.
- Using the quadratic formula - you find the coefficients and plug them into the formula:
For finding the coefficients you just need to look at the equation. Most likely the a will be the number before the x², the b will be the number before the x, and the c is the number by itself.
An example would be :
3x² + 4x - 56
a is 3, b is 4, and c is -56
Now to plug it into the quadratic formula, you just substitute the letters for the numbers.
x= -(4) ± √( 4² - 4(3)(-56))
————————
2(3)
Now you'd get x is equal to
-4 ± √ (16 + 672)
-4 ± √ (688)
——————
6
Now just a hint, when you get to this part of the equation you'll either get a rational or irrational/imaginary answer. But it depends on the discriminant (b² - 4ac).
So that's about it for solving equations.
Sources:
- John Schnatterly johnschnatterly.blogspot.com
- http://www.mathsisfun.com/definitions/quadratic-equation.html
- http://www.mathsisfun.com/algebra/quadratic-equation.html
No comments:
Post a Comment