Complex Numbers And Quadratic Equations question 549
Question: If $ \alpha ,\beta $ are the roots of the equation $ x^{2}+ax+b=0 $ then the value of $ {{\alpha }^{3}}+{{\beta }^{3}} $ is equal to [RPET 1989; Pb. CET 1991]
Options:
A) $ -(a^{3}+3ab) $
B) $ a^{3}+3ab $
C) $ -a^{3}+3ab $
D) $ a^{3}-3ab $
Show Answer
Answer:
Correct Answer: C
Solution:
Sum of root $ \alpha +\beta =-a $ and product of roots $ \alpha \beta =b $ So, $ {{\alpha }^{3}}+{{\beta }^{3}}=(\alpha +\beta )({{\alpha }^{2}}-\alpha \beta +{{\beta }^{2}}) $ = $ (\alpha +\beta )[{{(\alpha +\beta )}^{2}}-3\alpha \beta ]=-a(a^{2}-3b)=-a^{3}+3ab $
BETA
