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Question

# For the expression f(x) = a x2 + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value x0 is

A

f( ) > 0, < ( )

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B

f( ) < 0, ≥ ( )

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C

f( ) ≥ 0, < ( )

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D

f( ) > 0, = ( )

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Solution

## The correct option is A f( ) > 0, < ( ) As a > 0, graph is cup shaped parabola Consider the graph of f(x) in which roots of f(x) is shown to be greater than x0 . We know f(x0 ) > 0 Now, for x0 to be on left of α, & β, and also f(x0 ) > 0, we can comfortably take x0 < ( −b2a) So, A is right option.

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