Difference between revisions of "2002 AMC 12P Problems/Problem 23"

m (Solution)
m (Solution)
Line 15: Line 15:
  
 
== Solution ==
 
== Solution ==
According to Wolfram-Alpha, the answer is <math>A</math>
+
According to Wolfram-Alpha, the answer is <math>\boxed {\text{(A) }\sqrt{118}}</math>.
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2002|ab=P|num-b=22|num-a=24}}
 
{{AMC12 box|year=2002|ab=P|num-b=22|num-a=24}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 20:31, 10 March 2024

Problem

The equation $z(z+i)(z+3i)=2002i$ has a zero of the form $a+bi$, where $a$ and $b$ are positive real numbers. Find $a.$

$\text{(A) }\sqrt{118} \qquad \text{(B) }\sqrt{210} \qquad \text{(C) }2 \sqrt{210} \qquad \text{(D) }\sqrt{2002} \qquad \text{(E) }100 \sqrt{2}$

Solution

According to Wolfram-Alpha, the answer is $\boxed {\text{(A) }\sqrt{118}}$.

See also

2002 AMC 12P (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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
All AMC 12 Problems and Solutions

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