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Question

# For any quadratic expression f(x)=ax2+bx+c;a<0, having zeros as α,β and if k is any real number such that k<β<α, then select the correct statement(s).

A
b2a>k
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B
b2a<k
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C
D>0
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D
f(k)<0
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Solution

## The correct option is D f(k)<0Given quadratic expression as: f(x)=ax2+bx+c with a<0 α,β are roots of ax2+bx+c=0 and k is any real number such that: α>β>k Now, using the given conditions we can plot the graph as: From the graph, we can observe the following: (a) D>0, as f(x)=0 has two distinct real roots. (b) f(k)<0, from the graph. (c) Abscissa of Vertex =−b2a>k.

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