For any quadratic equation $y = a x^{2} + b x + c,$ if $a > 0 & D = 0,$ then $y < 0 \forall$

x \in R

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x \in R^{+}

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x \in ϕ

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Solution

The correct option is C $x \in ϕ$
Given quadratic equation: $y = a x^{2} + b x + c; a > 0 & D = 0$
Now, $a > 0$ means the graph is an upward opening parabola.
and $D = 0$ means the equation has only one root.
We can visualize the following as the graph shown as:

$\Rightarrow y \geq 0 \forall x \in R$
$\Rightarrow y < 0 \forall x \in ϕ$

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