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# Quadratic equations, which are expressed in the form of ax2

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions? Explain why.

Hi there,

An equation like that can have 0 real solutions, 1 real solution, or 2 real solutions.

You can tell by calculating the discriminant, which is equal to b^2-4ac. If that value is positive, then there are two real solutions. If it's zero, there is one real solution, and if it's negative, there are no real solutions.

When there are no real solutions, it means that there are two imaginary/complex solutions.

The reason you can have up to two solutions is that the quadratic equation has a +/- in it, so when you use the +, you can get a different solution than when you use the -. Unless, of course, the value after the +/- is equal to 0, in which case you get only a single solution.

Let me know if you have any questions,

Scott