A) \[a<0\]
B) \[{{b}^{2}}<4ac\]
C) \[c>0\]
D) a and b are of opposite signs
Correct Answer: A
Solution :
It is evident from the figure that the function \[y=a{{x}^{2}}+bx+c\] has a maximum between \[{{x}_{1}}\] and \[{{x}_{2}}\]. \[\therefore \,\,\,\frac{{{d}^{2}}y}{d{{x}^{2}}}<0\,\Rightarrow \]\[a<0\] Obviously,\[{{x}_{1}},{{x}_{2}}>0\]Þ \[{{x}_{1}}+{{x}_{2}}>0\] Þ Sum of the roots > 0 Þ \[\frac{-b}{a}>0\,\,\,\Rightarrow \frac{b}{a}<0\] Þ a and b are of opposite signs.
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