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Understanding Quadratic Equations for NECO

A quadratic equation is any equation that can be written as ax² + bx + c = 0, where a is not zero. NECO and WAEC test three main ways to solve these. Here's each one, plainly.

1. Factorization

Used when the equation splits neatly into two brackets. Find two numbers that multiply to give a × c and add to give b, then split the middle term using them.

2. Completing the square

Used when factorization isn't neat. You rewrite the equation so one side is a perfect square, then take the square root of both sides.

3. The quadratic formula

Works for every quadratic equation, no matter how messy: x = (-b ± √(b² - 4ac)) / 2a. If factorization looks difficult, go straight to this formula rather than wasting time.

Worked example

Question: Solve x² + 2x - 15 = 0
  1. Identify a = 1, b = 2, c = -15.
  2. Look for two numbers that multiply to -15 and add to 2: that's 5 and -3.
  3. Rewrite as (x + 5)(x - 3) = 0.
  4. Set each bracket to zero: x + 5 = 0 or x - 3 = 0.
  5. Solve each: x = -5 or x = 3.
Answer: x = -5 or x = 3
Exam tip: If you spend more than 30 seconds looking for factors without success, switch to the quadratic formula. It always works, and it's faster than guessing at factor pairs under time pressure.
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