1.1.3—Quadratic equations

A quadratic equation can be solved by factorising, completing the square or using x=(−b±√(b²−4ac))/(2a). All methods should return the same roots.

Factorise when integer or simple factors are visible; use the formula for a general or parameterised quadratic; complete the square when the vertex or inequality range is needed.

For 2x²+3x−2=0, factorising gives (2x−1)(x+2)=0, so x=1/2 or −2. The formula is a reliable check.

After multiplying or dividing an equation, preserve equivalence; taking a square root too early can lose the ± branch.