Complex Numbers And Quadratic Equations question 6
Question: If $ ax^{2}+bx+c=0 $ and $ bx^{2}+cx+a=0 $ have a common root $ a\ne 0 $ , then $ \frac{a^{3}+b^{3}+c^{3}}{abc}= $ [IIT 1982; Kurukshetra CEE 1983]
Options:
A) 1
B) 2
C) 3
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The condition for common roots gives $ {{(bc-a^{2})}^{2}}=(ca-b^{2})(ab-c^{2}) $ On simplification gives $ a^{3}+b^{3}+c^{3}=3abc $
BETA
