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How many solutions are possible for a quadratic equation? Are there
always 2 solutions? Why or why not?
There is only a maximum of 2 solutions for a quadratic equation. Since the highest degree of X or any other variable is 2, therefore, it will only give you a maximum of 2 solutions for X. If the number of solutions is greater than 2, it is not a quadratic equation. For example, if there are 3 solutions, then it is a cubic equation, not a quadratic equation.
You could simply get the number of solutions in an equation by using the formula: b²-4ac (a-quadratic term; b-linear term; c-constant term). If the result is positive, then you have two real solutions. If the result is positive perfect square, then you have two real rational solutions If the result is positive nonperfect square, then you have two irrational solutions If the result is zero, you have one real solution If the result is negative, no real solutions
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