Quadratic Equations

Quadratic equations arise in geometry, motion, area problems and algebraic modelling. Their standard form is ax² + bx + c = 0 with a ≠ 0.

A quadratic equation is identified by highest power 2 of the variable. Students should know how to rewrite word problems into standard form before solving.

When the quadratic can be split into two linear factors, each factor is equated to zero. This method is efficient for well-structured equations and strengthens factor sense.

The formula x = [-b ± √(b² - 4ac)] / 2a gives the roots for every quadratic equation. It is especially useful when factorisation is not easy or when roots are irrational.

The discriminant D = b² - 4ac tells us whether the roots are real and distinct, real and equal, or non-real. This is important both in theory and in quick problem analysis.

After this chapter, students should be able to identify quadratics, solve them by multiple methods, and interpret the discriminant meaningfully.