Make your own free website on Tripod.com

Strategies to solve Equations

What is quadratic???
Home
Questions/Answers
What is quadratic???

Enter subhead content here

 
Quadratic equations take the following form:
ax + bx + c = 0
Where X is the only variable and a, b and c are just numbers (constants, that may also be Zero!)
If a=0 then the equation is not quadratic: bx + c = 0
However, if b=0 then it can be: ax + c = 0
Whilst if c=0 then it's: ax + bx = 0
It is all much less confusing with numbers!
 
Quadratic Numbers
 
Normally, of course, equations like ax + bx + c = 0 are not written with a, b and c: they're usually just numbers.
e.g. 4x - 3x + 5 = 0
It's your job normally to find the valuesof x for which the equation works - nightmare!
Let's start with equations of the form: ax + c = 0
 
Solving equations like ax + c = 0 can be quite straightforward.
e.g.
x - 25 = 0
From your work on algebra, you should be able to rearrange the equation to: x =25
By taking the square-root of both sides, we end up with:
x = 5
That wasn't too bad, was it? Another solution is x = -5, but we'll look at that another time.
Here's one for you. Find the solution to the equation: x - 121 = 0.

 
could you find the solution to the equation: x - 121 = 0?
As with the previous example, we just need to rearrange the equation and find the square root:
x - 121 = 0

x = 121

x=11
of course another solution is x = -11
 
 
Let's now look at equations of the form ax + bx = 0
e.g. x+2x=0
If you know how to factorise, you'll be fine with this. We factorise the equation into:
x (x + 2) = 0
This could be true when x = 0, since 0 times the bracketed term = 0. However, there remains another possibility: the bracketed term itself is 0:
(x + 2) = 0
We can now ignore the brackets: x + 2 = 0
So the solution is: x = -2
So, the solutions to x + 2x = 0 are x = 0 or -2

Enter supporting content here