Difference between revisions of "1958 AHSME Problems/Problem 41"
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== Problem == | == Problem == | ||
| − | The roots of <math> Ax^2 | + | The roots of <math> Ax^2 + Bx + C = 0</math> are <math> r</math> and <math> s</math>. For the roots of |
<math> x^2+px +q =0</math> | <math> x^2+px +q =0</math> | ||
to be <math> r^2</math> and <math> s^2</math>, <math> p</math> must equal: | to be <math> r^2</math> and <math> s^2</math>, <math> p</math> must equal: | ||
| − | <math> \textbf{(A)}\ \frac{B^2 | + | <math> \textbf{(A)}\ \frac{B^2 - 4AC}{A^2}\qquad |
| − | \textbf{(B)}\ \frac{B^2 | + | \textbf{(B)}\ \frac{B^2 - 2AC}{A^2}\qquad |
| − | \textbf{(C)}\ \frac{2AC | + | \textbf{(C)}\ \frac{2AC - B^2}{A^2}\qquad \\ |
| − | \textbf{(D)}\ B^2 | + | \textbf{(D)}\ B^2 - 2C\qquad |
| − | \textbf{(E)}\ 2C | + | \textbf{(E)}\ 2C - B^2</math> |
| − | |||
== Solution == | == Solution == | ||
Revision as of 22:25, 13 March 2015
Problem
The roots of 
are 
and 
. For the roots of
to be 
and 
, 
must equal:
Solution
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 40 |
Followed by Problem 42 | |
| 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. 
