Complex Numbers And Quadratic Equations question 554
Question: The sum of the roots of a equation is 2 and sum of their cubes is 98, then the equation is [MP PET 1986]
Options:
A) $ x^{2}+2x+15=0 $
B) $ x^{2}+15x+2=0 $
C) $ 2x^{2}-2x+15=0 $
D) $ x^{2}-2x-15=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let roots are $ \alpha $ and $ \beta $ $ \alpha +\beta =2 $ and $ {{\alpha }^{3}}+{{\beta }^{3}}=98 $ \ $ {{\alpha }^{3}}+{{\beta }^{3}}=(\alpha +\beta )({{\alpha }^{2}}-\alpha \beta +{{\beta }^{2}}) $
Þ $ 98=2[ {{(\alpha +\beta )}^{2}}-3\alpha \beta ]\Rightarrow 49=(4-3\alpha \beta ) $
Þ $ \alpha \beta =-15 $ Thus equation is $ x^{2}-2x-15=0 $ .
BETA
