Complex Numbers And Quadratic Equations question 185
Question: If 8, 2 are the roots of $ x^{2}+ax+\beta =0 $ and 3, 3 are the roots of $ x^{2}+\alpha x+b=0 $ , then the roots of $ x^{2}+ax+b=0 $ are [EAMCET 1987]
Options:
A) $ 8,-1 $
B) - 9, 2
C) $ -8,-2 $
D) 9, 1
Show Answer
Answer:
Correct Answer: D
Solution:
8, 2 are the roots of $ x^{2}+ax+\beta =0 $ \ $ 8+2=10=-a $ , $ 8.2=16=\beta $ i.e. $ a=-10,\beta =16 $ 3, 3 are the roots of $ x^{2}+\alpha x+b=0 $ \ $ 3+3=6=-\alpha ,3.3=b $ i.e. $ \alpha =-6,b=9 $ Now, $ x^{2}+ax+b=0 $ becomes $ x^{2}-10x+9=0 $ or $ (x-1)(x-9)=0\Rightarrow x=1,9 $ .
BETA
