Complex Numbers And Quadratic Equations question 819
Question: If a, b, g are the roots of the equation $ 2x^{3}-3x^{2}+6x+1=0 $ , then $ {{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}} $ is equal to [Karnataka CET 2005]
Options:
A) - $ \frac{15}{4} $
B) $ \frac{15}{4} $
C) $ \frac{9}{4} $
D) 4
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation $ 2x^{3}-3x^{2}+6x+1=0 $ $ \alpha +\beta +\gamma =\frac{3}{2} $ , $ \alpha \beta \gamma =\frac{-1}{2} $ , $ \Sigma \alpha \beta =3 $ $ ({{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}})={{(\alpha +\beta +\gamma )}^{2}}-2(\Sigma \alpha \beta ) $ = $ {{( \frac{3}{2} )}^{2}}-2.3 $ = $ \frac{9}{4}-6=\frac{-15}{4} $ .
BETA
