This is a clever formula that you can use on a quadratic equation that will almost always solve it. It seems a bit complicated at first, but is very easy to use once you get used to it. It runs as follows:
If you have a quadratic equation in the general form:
Then to find the solutions, use the values of a, b and c in the following formula:
To help you understand it, let’s use it on the first quadratic equation we saw:
For this equation, a = 1, b = 3 and c = 2. So:
And how we got our answers previously is revealed! Note how a ‘±’ sign means that there are actually two solutions, one for when it is a ‘+’, and one for when it is a ‘–‘. Also note how ‘nice’ the solutions are – they don’t have any decimal or fraction parts. This is not always the case.
Sometimes you get a negative number underneath the square root sign in the formula. If this happens, then you can’t solve the quadratic equation – the quadratic equation has no real solutions. (There are ‘imaginary’ solutions, but you don’t need to know how to get them – just say there is no solution).