- You'll have to work a little harder to crack them
- You'll get many more marks in exams when you do!
Don't worry why they're called quadratic - it basically means "involving squared powers".
What's a Quadratic?
Quadratic equations take the following form:
ax² + 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: ax² + c = 0
Whilst if c=0 then it's: ax² + bx = 0
It is all much less confusing with numbers!
Quadratics With Numbers
Normally, of course, equations like ax² + bx + c = 0 are not written with a, b and c: they're usually just numbers.
e.g. 4x² - 3x + 5 = 0
It's your job normally to find the values of x for which the equation works - nightmare!
Let's start with equations of the form: ax² + c = 0
Solving Quadratic Equations
Solving equations like ax² + c = 0 can be quite straightforward.
e.g. x² - 25 = 0
From your work on algebra, you should be able to rearrange the equation to: x² = 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: x² - 121 = 0.
Once you've worked it out, click here.
