What is the quadratic equation and what does it do?
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As mentioned by some others, the quadratic equation is just the formula for finding x when an equation looks like:
ax^2 + bx + c = 0
The process of finding this formula is straightforward and anyone who has just completed an Algebra class in Middle or High school should be able to do it.
However, in addition to being a useful formula for finding x in its own right, it also has a useful property of giving us information about the solution without having to fully solve it.
In the formula (which is repeated in many other answers), the part under the square root sign is:
b^2 – 4ac
Just solving this part by itself tells us about the values of x we will find if we fully solve for x.
This value by itself is called the determinant. If it is positive, there are 2 real values for x. If it is 0, there is only 1 real value for x. If it is negative, then there are no real values for x. What the last part means is that there is no real number value for x that will satisfy the equation.
This means only part of the formula needs to be solved to know if there is actually a possible real number solution.
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