Lessons · Quantitative Reasoning

CLT Quantitative Reasoning · Lesson

Quadratics

A quadratic has an x² term. Factor it, use the special patterns, or use the vertex. Many CLT-style questions are faster with a pattern than with the formula.

How to do it
  1. Set the equation equal to 0, then factor: find two numbers that multiply to c and add to b.
  2. Know the patterns: a² − b² = (a + b)(a − b), (a + b)² = a² + 2ab + b².
  3. For the vertex of y = ax² + bx + c, x = −b ÷ 2a. That gives the minimum or maximum.
  4. The sum of the roots is −b/a and the product is c/a.
Example

Q. If a + b = 13 and a − b = 5, what is a² − b²?

Answer 65

a² − b² = (a + b)(a − b) = 13 × 5. No need to find a and b.

Traps
  • Dividing both sides by x and losing the root x = 0.
  • Forgetting the negative root: x² = 25 means x = 5 or x = −5.
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