For the equation a $x^{2}$ + bx + c = 0 having 2 real roots, one root lies between real values $x_{1}$ & $x_{2}$ if

< <

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< c- <

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f( ) f( ) < 0

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f() f() > 0

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Solution

The correct option is C
f( ) f( ) < 0

Let a > 0, graph of f(x) is upward (cup shaped)parabola.

Let α be the root of f(x) between $x_{1}$ & $x_{2}$

From graph, f( $x_{1}$ ) > 0 and f( $x_{2}$ ) < 0

So, f( $x_{1}$ ) f( $x_{2}$ ) < 0. Similarly, for a<0, the same condition can be proved.

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For the equation a x2 + bx + c = 0 having 2 real roots, one root lies between real values x1 & x2 if

The correct option is C f( ) f( ) < 0 Let a > 0, graph of f(x) is upward (cup shaped)parabola. Let α be the root of f(x) between x1 & x2 From graph, f( x1) > 0 and f( x2) < 0 So, f( x1) f( x2) < 0. Similarly, for a<0, the same condition can be proved.

For the equation a $x^{2}$ + bx + c = 0 having 2 real roots, one root lies between real values $x_{1}$ & $x_{2}$ if

The correct option is C
f( ) f( ) < 0

Let a > 0, graph of f(x) is upward (cup shaped)parabola.

Let α be the root of f(x) between $x_{1}$ & $x_{2}$

From graph, f( $x_{1}$ ) > 0 and f( $x_{2}$ ) < 0

So, f( $x_{1}$ ) f( $x_{2}$ ) < 0. Similarly, for a<0, the same condition can be proved.