Quadratic Equation Solver
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If you have an equation of the form "ax2 + bx + c = 0", we can solve it for you. Just enter the factors a, b and c below, and press "Get Results" |
Is it Quadratic?
Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.
The name comes from "quad" meaning square, So, the biggest clue is that highest power must be a square (in other words x2).
These are all quadratic equations in disguise:
| In disguise | In standard form | a, b and c |
|---|---|---|
| x2 = 3x -1 | x2 - 3x + 1 = 0 | a=1, b=-3, c=1 |
| 2(x2 - 2x) = 5 | 2x2 - 4x - 5 = 0 | a=2, b=-4, c=-5 |
| x(x-1) = 3 | x2 - x - 3 = 0 | a=1, b=-1, c=-3 |
| 5 + 1/x - 1/x2 = 0 | 5x2 + x - 1 = 0 | a=5, b=1, c=-1 |
How does this work?
The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:
![x = [ -b plus minus square root of (b^2-4ac) ] / 2a](algebra/images/quadratic-formula.svg)
The "±" means you need to do a plus AND a minus, so there are normally TWO solutions !
The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer. If it is positive, you will get two normal solutions, if it is zero you get just ONE solution, and if it is negative you get imaginary solutions.