Difference between revisions of "1959 AHSME Problems/Problem 27"

(The solution was missing)
(see also box, improved solution)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
 +
== 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 1
+
== Solution ==
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.
+
 
 +
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>.
 +
 
 +
== 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 $ix^2-x+2i=0$, 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

By Vieta's Formulas, the sum of the roots is $\frac{1}{i} = -i$, which is not $2$, so the solution is $\fbox{\textbf{(A)}}$.

See also

1959 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 26
Followed by
Problem 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png