2006 AMC 10B Problems/Problem 14
Problem
Let and be the roots of the equation . Suppose that and are the roots of the equation . What is ?
Video Solution
https://youtu.be/3dfbWzOfJAI?t=457
~ pi_is_3.14
Solution
In a quadratic equation of the form , the product of the roots is (Vieta's Formulas).
Using this property, we have that and
.
- Notice the fact that we never actually found the roots.
Solution 2
Assume without loss of generality that . We can factor the equation into . Therefore, and . Using these values, we find and . By Vieta's formulas, is the product of the roots of , which are and . Therefore, .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AMC 10 Problems and Solutions |
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