      Strategies to solve Equations What is 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!   Quadratic 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. 4•x² - 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: ax² + c = 0   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.   •could you find the solution to the equation: x² - 121 = 0? •As with the previous example, we just need to rearrange the equation and find the square root: x² - 121 = 0 x² = 121 x=11 of course another solution is x = -11     •Let's now look at equations of the form ax² + bx = 0 e.g. x²+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 x² + 2x = 0 are x = 0 or -2     