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Quadratic equations – Double Solutions, Imaginary Solutions and Just Plain Wrong

Sometimes I find myself lying awake at night, thinking about stuff. Last night, I was kept awake by the realisation that I had forgotten how to solve quadratic equations, which is something which would have been routine for me as a schoolboy.

The quadratic equation is something in this form:

ax² + bx + c = 0  

You get told what a, b and c are, and you have to work out what x is. So I looked it up to remind myself of the formula. It is thus:

x = [-b ± √(b² − 4ac)] / (2a)  

It all came flooding back. The bit inside the square root is known as the discriminant. If it is positive, then there are two possible answers. If it is 0, then there is just one answer. If it is negative, then you get imaginary solutions – i.e. in the weird territory to which the door is the square root of -1.[1]  

SuperGrok gave me some examples, thus:  

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