1959 AHSME Problems/Problem 27: Difference between revisions
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== Problem == | |||
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 13:01, 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 
.
