Complex Numbers And Quadratic Equations question 22
If the roots of $ x^{2}+x+a=0 $ exceed 1, then [EAMCET 1994]
Options:
A) $ 2<a<3 $
B) $ a>3 $
C) $ -3<a<3 $
D) $ a<-2 $
Show Answer
Answer:
Correct Answer: D
Solution:
If the roots of the quadratic equation $ ax^{2}+bx+c=0 $ exceed a number k, then $ ak^{2}+bk+c>0 $ if $ a>0, $ $ b^{2}-4ac\ge 0 $ and sum of the roots $ >2k $ Therefore, if the roots of $ x^{2}+x+a=0 $ exceed a number a, then $ a^{2}+a+a>0,1-4a\ge 0 $ and $ -1>2a $
Þ $ a(a+2)>0, $ $ a\le \frac{1}{4} $ and $ a<-\frac{1}{2} $
Þ $ a>0 \text{ or } a<-2, a<\frac{1}{4} $ and $ a<-\frac{1}{2} $ Hence $ a<-2 $ .
BETA
