lf $α, β$ are the real roots of the equation $a x^{2} + b x + c = 0$ , then the value of $(1 + α + α^{2}) (1 + β + β^{2})$ is

positive

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negative

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non-negative

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non-positive

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Solution

The correct option is B positive
If we see the expression $(1 + α + α^{2}) (1 + β + β^{2})$
The discriminant of both the expressions $(1 + α + α^{2})$ & $(1 + β + β^{2})$ is less than zero, which means the expression will always give a positive value more than zero .
So, the expression will always be positive .
Option A is correct .

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