Difference between revisions of "1959 AHSME Problems/Problem 27"
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Which one of the following is not true for the equation <math>ix^2-x+2i=0</math>, where <math>i=\sqrt{-1}</math> <math>\textbf{(A)}\ \text{The sum of the roots is 2} \qquad \\ \textbf{(B)}\ \text{The discriminant is 9}\qquad \\ \textbf{(C)}\ \text{The roots are imaginary}\qquad \\ \textbf{(D)}\ \text{The roots can be found using the quadratic formula}\qquad \\ \textbf{(E)}\ \text{The roots can be found by factoring, using imaginary numbers}</math> | Which one of the following is not true for the equation <math>ix^2-x+2i=0</math>, where <math>i=\sqrt{-1}</math> <math>\textbf{(A)}\ \text{The sum of the roots is 2} \qquad \\ \textbf{(B)}\ \text{The discriminant is 9}\qquad \\ \textbf{(C)}\ \text{The roots are imaginary}\qquad \\ \textbf{(D)}\ \text{The roots can be found using the quadratic formula}\qquad \\ \textbf{(E)}\ \text{The roots can be found by factoring, using imaginary numbers}</math> | ||
− | Solution | + | == Solution == |
− | + | ||
+ | By [[Vieta's Formulas]], the sum of the roots is <math>\frac{1}{i} = -i</math>, which is not <math>2</math>, so the solution is <math>\fbox{\textbf{(A)}}</math>. | ||
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+ | == See also == | ||
+ | {{AHSME 50p box|year=1959|num-b=26|num-a=28}} | ||
+ | {{MAA Notice}} |
Latest revision as of 12:29, 21 July 2024
Problem
Which one of the following is not true for the equation , where
Solution
By Vieta's Formulas, the sum of the roots is , which is not , so the solution is .
See also
1959 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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