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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>
  
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Solution 1
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== Solution ==
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The sum of the roots can be calculated by -b/a. For this equation, that is 1/i=-i, which is not 2, so the solution is A.
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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 $ix^2-x+2i=0$, where $i=\sqrt{-1}$ $\textbf{(A)}\ \text{The sum of the roots is 2} \qquad \\ \textbf{(B)}\ \text{The discriminant is 9}\qquad \\ \textbf{(C)}\ \text{The roots are imaginary}\qquad \\ \textbf{(D)}\ \text{The roots can be found using the quadratic formula}\qquad \\ \textbf{(E)}\ \text{The roots can be found by factoring, using imaginary numbers}$

Solution

The sum of the roots can be calculated by $-\frac{b}{a}$. For this equation, that is $\frac{1}{i} = -i$, which is not $2$, so the solution is $\boxed{A}$.

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