Solving Quadratic Equations

Quadratics take the form ax² + bx + c = 0.

You can solve by factorising (when factors are integers) or using the quadratic formula

𝑥 = (−𝐵 ± √(𝐵² − 4𝐴𝐶)) / (2𝐴)

Quadratics appear in more advanced puzzles like hard Tangle Traps or Equation Detective scenarios involving area or rate problems.

Always start by seeing if simple factorisation works; it’s faster and reinforces the link between expansion and root-finding. If not, the formula handles all cases, including irrational or repeated roots.

Example: Solve x² − 5x + 6 = 0

1. Factorise: (x − 2)(x − 3) = 0
2. Set each factor to zero: x = 2 or x = 3

Hints and tips

• Always check for factorisation first: Attempt (x + p)(x + q) = 0 before using the quadratic formula.
• Apply the quadratin formula carefully: Underline the entire numerator during substitution to ensure you include −b.
• Simplify radicals: Factor perfect squares from D to simplify square root of D when possible.
• Verify context: If a puzzle only allows one positive integer root, discard the other solution accordingly.