Difference between revisions of "1959 AHSME Problems/Problem 27"
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+ | == Problem == | ||
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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 == |
− | The sum of the roots can be calculated by -b/ | + | |
+ | The sum of the roots can be calculated by <math>-\frac{b}{a}</math>. For this equation, that is <math>\frac{1}{i} = -i</math>, which is not <math>2</math>, so the solution is <math>\boxed{A}</math>. |
Revision as of 14:01, 16 July 2024
Problem
Which one of the following is not true for the equation , where
Solution
The sum of the roots can be calculated by . For this equation, that is
, which is not
, so the solution is
.