Complex Numbers And Quadratic Equations question 548
Question: If the roots of the equation $ x^{2}+x+1=0 $ are $ \alpha ,\beta $ and the roots of the equation $ x^{2}+px+q=0 $ are $ \frac{\alpha }{\beta },\frac{\beta }{\alpha } $ then $ p $ is equal to [RPET 1987]
Options:
A) -2
B) -1
C) 1
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ \alpha $ and $ \beta $ be the roots of $ x^{2}+x+1=0 $ , so $ \alpha +\beta =-1 $ and $ \alpha \beta =1 $ Again $ \frac{\alpha }{\beta } $ and $ \frac{\beta }{\alpha } $ are the roots of $ x^{2}+px+q=0, $ so $ \frac{\alpha }{\beta }+\frac{\beta }{\alpha }=-p $
Þ $ -p=\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta } $
Þ $ -p=\frac{{{(\alpha +\beta )}^{2}}-2\alpha \beta }{\alpha \beta }=\frac{1-2}{1}\Rightarrow p=1 $
BETA
