Common Algebra Mistakes
Example: Solving a Quadratic Equation |
The Goal
Solve the following equation for t:
The Mistake
Find the algebra mistake: (Roll the mouse over the algebra to see a hint in red) The Correction
(Roll the mouse over the area above to see the correction in blue) An Explanation
It is no help in solving a quadratic equation to arrange it in the form at^{2} + bt = c (unless c = 0) (in this problem, t^{2} - 6t = 3) and then write it in the form t(at + b) = c (in this problem, t(t - 6) = 3). If c is not 0, you cannot conclude that t = c or at + b = c (in this case t = 3 or t - 6 = 3). In this problem you can check that neither 3 nor 9 are solutions of the original equation.
(see The Correction for the solution to the equation t^{2} - 6t - 3 = 0 using the quadratic formula) |
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