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\[f\left( 1 \right)>0\therefore a+b+c>0\].