Quadratic Equation & Inequality Solver

• Type the coefficients a, b and c of ax² + bx + c = 0.
• The tool computes the discriminant b² − 4ac and tells you the type of roots.
• It solves for the roots and sketches the parabola with the roots marked.

Seeing the discriminant, the roots and the graph together builds real understanding, not just an answer to copy.

Quadratics sit near the heart of Form 4 Add Math, and this tool is built to show the connections the exam expects you to understand, not just to hand back a number. The discriminant b² − 4ac decides the nature of the roots before you solve anything: positive means two distinct real roots, zero means one repeated root, and negative means no real roots, which on the graph is a parabola that never crosses the x-axis.

Watching the sketch change as you adjust a, b and c makes those cases concrete, and links the algebra to the shape in a way a printed answer cannot. Use it to check your own working and to build intuition, but do the working yourself first: in the exam you must show the method, and the tool is here to confirm and illuminate your steps, not to replace them.

For inequalities, the roots and the sketch together show which region satisfies the inequality, the part of the parabola above or below the axis.

A quick tool is genuinely useful, but it is worth being clear about what it can and cannot do. It can check a result, illustrate an idea, or save time on planning, but the SPM exam rewards method, not answers, and marks come from working you produce yourself under exam conditions.

So use a tool the way you would use the answer at the back of a book: attempt the problem first, then use the tool to confirm your result or to see where your working went wrong. A student who leans on a tool to avoid the working tends to feel confident right up until the exam, where no tool is allowed and the method has to come from memory and practice.

Used the other way, to check and to build intuition, the same tool speeds up real learning. If you find you can get an answer from the tool but cannot yet reproduce the steps yourself, that gap is exactly what a lesson is for.