For any quadratic expression $y = a x^{2} + b x + c,$ where $a > 0 & D < 0, y < 0$ for

x \in R^{+}

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x \in ϕ

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x \in R^{-}

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Solution

The correct option is B $x \in ϕ$
Given quadratic equation $y = a x^{2} + b x + c$ where $a > 0 & D < 0.$
Now, if $D < 0 \Rightarrow$ The equation will have no real roots.
Also, $a > 0 \Rightarrow$ The graph will be an upward opening parabola as shown:

Thus, from the graph $y > 0 \forall x \in R .$
$∴ y < 0 \forall x \in ϕ .$

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