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Question

Forf(x)=ax2+bx+c,a0, the conditions for which the graph is a downward opening parabola and f(x)=0 have a unique root with multiplicity 2 is

A
a<0,D<0
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B
a<0,D=0
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C
a>0,D=0
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D
a>0,D<0
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Solution

The correct option is B a<0,D=0
Given: f(x)=ax2+bx+c,a0
For graph to be a downward opening parabola we must have a<0
Also, the equation has one root with a multiplicity 2. This means the equation has identical real roots which occurs when discriminant D=0.

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