Complex Numbers And Quadratic Equations question 201
Question: If a, b, g are roots of equation $ x^{3}+ax^{2}+bx+c=0 $ , then $ {{\alpha }^{-1}}+{{\beta }^{-1}}+{{\gamma }^{-1}}= $ [EAMCET 2002]
Options:
A) a/c
B) - b/c
C) b/a
D) c/a
Show Answer
Answer:
Correct Answer: B
Solution:
a, b, g are the roots of the equation $ x^{3}+ax^{2}+bx+c=0 $ so $ \alpha +\beta +\gamma =-a $ , $ \alpha \beta +\beta \gamma +\gamma \alpha =b $ and $ \alpha \beta \gamma =-c $ Now $ {{\alpha }^{-1}}+{{\beta }^{-1}}+{{\gamma }^{-1}} $ $ =\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma } $ $ =\frac{\alpha \beta +\beta \gamma +\gamma \alpha }{\alpha \beta \gamma } $ $ =-b/c $ .
BETA
