Theory of Quadratic Equations: Practice

The discriminant b² − 4ac decides the nature of a quadratic's roots, and for ax² + bx + c = 0 the roots have sum −b/a and product c/a. This practice sheet has three sections: A on the discriminant and nature of roots, B on sum and product of roots (including α² + β²), and C on forming equations from given roots, with every step shown.