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Question

If both the roots α,β of the quadratic equation ax2+bx+c=0,a<0 are less than a real number k such that k>α>β Considering f(x)=ax2+bx+c, select the correct statement(s).

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

The correct option is C D>0Given the quadratic polynomial: f(x)=ax2+bx+c,a<0 Let α,β be it's roots of f(x)=0. Now, k is a real number such that k>α>β So, we can draw the graph as: Clearly, for this to happen, the following conditions needs to be satisfied: (a) D>0 because f(x)=0 has 2 distinct roots. (b) f(k)<0. (c) Abscissa of Vertex =−b2a<k

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