Difference between revisions of "1995 AIME Problems/Problem 5"
m |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | For certain real values of <math>\displaystyle a, b, c,</math> and <math>\displaystyle d,</math> the equation <math>\displaystyle x^4+ax^3+bx^2+cx+d=0</math> has four non-real roots. The product of two of these roots is <math>\displaystyle 13+i</math> and the sum of the other two roots is <math>\displaystyle 3+4i,</math> where <math>i=\sqrt{-1}.</math> Find <math>\displaystyle b.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_4|Previous Problem]] | ||
| + | * [[1995_AIME_Problems/Problem_6|Next Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 01:06, 22 January 2007
Problem
For certain real values of 
and 
the equation 
has four non-real roots. The product of two of these roots is 
and the sum of the other two roots is 
where 
Find 
