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Difference between revisions of "1971 Canadian MO Problems"

(→‎Problem 5)
(→‎Problem 4)
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== Problem 4 ==
 
== Problem 4 ==
  
 +
Determine all real numbers <math>a</math> such that the two polynomials <math>x^2+ax+1</math> and <math>x^2+x+a</math> have at least one root in common.
  
  
 
[[1971 Canadian MO Problems/Problem 4 | Solution]]
 
[[1971 Canadian MO Problems/Problem 4 | Solution]]
 +
 
== Problem 5 ==
 
== Problem 5 ==
  

Revision as of 11:53, 8 October 2007

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Problem 1

$DEB$ is a chord of a circle such that $DE=3$ and $EB=5 .$ Let $O$ be the center of the circle. Join $OE$ and extend $OE$ to cut the circle at $C.$ Given $EC=1,$ find the radius of the circle

CanadianMO 1971-1.jpg


Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Determine all real numbers $a$ such that the two polynomials $x^2+ax+1$ and $x^2+x+a$ have at least one root in common.


Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Resources

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