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Q&A #104 |
From: Daniel Springer
To: Teacher2Teacher Public Discussion
Date: 2009020319:44:24
Subject: trinomial factoring redered trivial by simple method (Can even be done mentally)
I have never seen this in Mathematics Teacher or any other source. The method renders mentally solving (or factoring) reasonable quadratics nearly trival. EXAMPLE: If, 20x^2 + 28x - 3 = 0 THINK: "product = 60, differ by 28, want smaller number" AHA! "2 and 30" Thus, x = 2/20 or -30/20 DONE! In general, if ax^2 + bx + c = 0, a is positive Then, ax(ax + b) = -c We think of a pair of numbers that differ by b whose product is -c, lets say the pair is {P, Q}, then {-P, -Q} also satisfy the equation. We decide if ax is larger or smaller than (ax + b). This is easy, if b > 0 then ax is smaller, otherwise ax is larger. Suppose that ax is smaller and P is the smaller number, then Then, our answer is: x = P/a or x = -Q/a
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