Complex Numbers And Quadratic Equations question 590
Question: The value of p for which one root of the equation $ x^{2}-30x+p=0 $ is the square of the other, are [Roorkee Qualifying 1998]
Options:
A) 125 only
B) 125 and $ -216 $
C) 125 and 215
D) 216 only
Show Answer
Answer:
Correct Answer: B
Solution:
$ \alpha +{{\alpha }^{2}}=30 $ and $ {{\alpha }^{3}}=p $ $ {{\alpha }^{2}}+\alpha -30=0\Rightarrow (\alpha +6)(\alpha -5)=0 $ Þ $ \alpha =-6,5 $ \ $ p={{\alpha }^{3}}={{(-6)}^{3}}=-216 $ and $ p={{(5)}^{3}} $ = 125 $ p=125 $ and $ -216 $ .
BETA
