10th Class
Mathematics
Related to Competitive Exam
Question Bank
Quadratic Inequation
question_answer
If the roots of \[a{{x}^{2}}+bx+c=0,a>0,\] be each greater than unity, then:
A) \[a+b+c=0\]
B) \[a+b+c>0\]
C) \[a+b+c<0\]
D) None of these
Correct Answer:
A
Solution :
(a): Let \[f(x)=a{{x}^{2}}+bx+c\]. Appreciation of graph will help us solve the problem. Since,\[~\alpha >1\] and \[~\beta >1\], therefore, from figure, we can appreciate that\[f\left( 1 \right)>0\therefore a+b+c>0\].