Maths · Quadratic equations. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A quadratic equation has the standard form ax2 + bx + c = 0 with a ≠ 0. It has two roots, which can be found by factorisation, by completing the square or by the quadratic formula.
Many other equations become quadratic after a substitution. For x4 − 13x2 + 36 = 0 put y = x2; for an exponential equation in 22x and 2x put y = 2x. Solve for y, then go back and find x.
A radical equation has the unknown under a root sign. Squaring both sides removes the root but can bring in an extraneous root, so every answer must be checked in the original equation.
After squaring a radical equation students accept both roots of the quadratic. Put each one back into the original equation and reject any that does not satisfy it.
Answer: Solution set = {3}
Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.
← Systems of linear equationsRoots of unity and polynomial theorems →Take a Maths test