Complex Numbers And Quadratic Equations question 191
Question: For the equation $ 3x^{2}+px+3=0,p>0 $ if one of the root is square of the other, then p is equal to [IIT Screening 2000]
Options:
A) $ \frac{1}{3} $
B) 1
C) 3
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \alpha +{{\alpha }^{2}}=-\frac{p}{3} $ and $ \alpha .{{\alpha }^{2}}=1. $ So $ \alpha =1, $ $ \omega ,{{\omega }^{2}} $ . If $ \alpha =1,p<0 $ . If $ \alpha =\omega or{{\omega }^{2}}, $ we have $ \omega +{{\omega }^{2}}=-\frac{p}{3} $
Þ $ -1=\frac{-p}{3}\Rightarrow p=3 $ .
BETA
