Linear Equations

Form: ax + b = c

Solved by isolating x: x = (c - b) / a. Always has exactly one solution unless a = 0 (no solution or infinite solutions).

Quadratic Equations

Form: ax² + bx + c = 0

Solved using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The discriminant determines the nature of solutions.

Discriminant Analysis

Δ = b² - 4ac

• • Δ > 0: Two distinct real roots
• • Δ = 0: One repeated real root
• • Δ < 0: Two complex conjugate roots

Verification

Always check your solutions

Substitute each solution back into the original equation to verify that both sides are equal. This confirms the solution is correct.