Complex Numbers And Quadratic Equations question 557
Question: The roots of the equation $ x^{2}+ax+b=0 $ are p, and q, then the equation whose roots are $ p^{2}q $ and $ pq^{2} $ will be [MP PET 1980]
Options:
A) $ x^{2}+abx+b^{3}=0 $
B) $ x^{2}-abx+b^{3}=0 $
C) $ bx^{2}+x+a=0 $
D) $ x^{2}+ax+ab=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=x^{2}+ax+b=0 $ Þ $ p+q=-a $ and $ pq=b $ Now required equation whose roots are $ p^{2}q $ and $ pq^{2} $ Therefore sum of roots $ =p^{2}q+pq^{2}=pq(p+q)=-ab $ and product of roots = $ pq^{2}.qp^{2}={{(pq)}^{3}}=b^{3} $ Thus equation is $ x^{2}+abx+b^{3}=0 $ .
BETA
