Instructions
Enter coefficients, get the equation solved!
This quadratic equation solver lets you see worked solutions to quadratic equations.
You can see worked solutions using factorisation, the quadratic formula, or completing the square.
A quadratic is any equation of the form \(ax^2 + bx + c = 0\). Quadratics have up to two "roots", or values
of \(x\) which satisfy the equation. The three common methods for finding these roots are:
- Factorisation: by inspection, work out what the required values of \(x\) are, and factorise the equation into the form \((x + x_1)(x + x_2)=0\), where \(-x_1\) and \(-x_2\) are the roots. These values are the roots because they cause one of the bracketed terms to equal zero, satisfying the equation.
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Quadratic Formula: by memorising the quadratic formula, you can solve any quadratic equation. The roots \(x_1\) and \(x_2\) of a quadratic equation can be found using
\[x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] - Completing the square: the quadratic equation can be rearranged into the form \((x-h)^2+k=0\), from which the roots are \(x_{1,2}=h \pm \sqrt{-k}\).
Input an equation or click to generate a random equation, and then choose a method to see the worked solution.
Negative \(x^2\) coefficient
You cannot input a negative \(x^2\) coefficient using this tool. However, you can use the fact that \[-ax^2 + bx + c = 0 \Rightarrow ax^2 + (-b)x + (-c) = 0\] This is achieved by multipling both sides by \(-1\), which is convenient since the right hand side is zero.
Glitches and Improvements
If you find any glitches or have ideas for how this applet could be improved, please let me know by contacting me on Twitter: @NextLevelMaths.
