Difference between revisions of "1959 AHSME Problems/Problem 27"
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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> | |
| − | The sum of the roots can be | + | |
| + | == 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>. | ||
| + | |||
| + | == 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 | |
| 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. 
