Graphs of Quadratic Equation for different values of D when a>0
Consider fx=a...
Question
Consider f(x)=ax2+bx+c with a>0,
If both roots of the quadratic equation are smaller than any constant k. The necessary and sufficient condition for this are :
A
−b2a<k
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B
D≥0
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C
All of the above
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D
f(k)>0
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Solution
The correct option is Df(k)>0
Let, α,β be the roots of f(x)=ax2+bx+c=0
When both roots of f(x)=0 are smaller than k.
From graph,
D>0 when roots are real and distinct, and D=0 when roots are real and equal.