Complex Numbers And Quadratic Equations question 816
Question: If $ \alpha ,\beta ,\gamma $ are the roots of the equation $ x^{3}+x+1=0 $ , then the value of $ {{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}} $ [MP PET 2004]
Options:
A) 0
B) - 3
C) 3
D) - 1
Show Answer
Answer:
Correct Answer: D
Solution:
We know that the roots of the equation $ ax^{3}+bx^{2}+cx+d=0 $ follows $ \alpha \beta \gamma =-d/a $ Comparing above equation with given equation we get $ d=1,a=1 $ So, $ \alpha \beta \gamma =-1 $ or $ {{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}=-1 $ .
BETA
