For the expression $f (x) = a x^{2} + b x + c, (a > 0)$ , the condition for both real roots of $f (x)$ to be greater than (or) lesser than a real value $M$ is,

$f (M) < 0$

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$f (M) \leq 0$

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$f (M) \geq 0$

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$f (M) > 0$

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Solution

The correct option is D
$f (M) > 0$

As $a > 0$ , graph of $f (x)$ is cup shaped parabola.

For $M$ to be less than both roots (or) greater than both roots see that $f (M) > 0$ .

So, option $A$ is true.

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For the expression f(x)=ax2+bx+c,(a>0), the condition for both real roots of f(x) to be greater than (or) lesser than a real value M is,

The correct option is D f(M)>0 As a>0, graph of f(x) is cup shaped parabola. For M to be less than both roots (or) greater than both roots see that f(M)>0. So, option A is true.

For the expression $f (x) = a x^{2} + b x + c, (a > 0)$ , the condition for both real roots of $f (x)$ to be greater than (or) lesser than a real value $M$ is,

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As $a > 0$ , graph of $f (x)$ is cup shaped parabola.

For $M$ to be less than both roots (or) greater than both roots see that $f (M) > 0$ .

So, option $A$ is true.