Complete the square, and turn it into the quadratic formula that solves every quadratic equation. Then read the discriminant to know, before solving, whether there are two roots, one or none.
3 lessons, about 1 h 10 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabSome quadratic equations do not factorise neatly. Completing the square solves them all. We add the number that turns into a perfect square, , then take the square root of both sides. A picture of a square with one corner missing shows why it works.
Completing the square on once and for all gives the quadratic formula, . It solves every quadratic equation. We derive it, use it on equations and on a problem about a thrown ball, and check the answers.
The number under the root decides the roots before we solve. It is called the discriminant, . If there are two distinct real roots, if two equal roots, and if no real roots. We use it to find unknown numbers and to decide whether a design is possible.
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