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Relative Position of a Point with Respect to a Line

If x-1 x-2x...

Question

If $(x - 1) (x - 2) (x + 5) < 0$ , then

x < - 3, 0 < x < 2

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x < - 5, 1 < x < 2

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x > 2, - 5 < x < 1

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x < 1, - 5 < x < 2

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Solution

The correct option is A $x < - 5, 1 < x < 2$
The points where curve $f (x) = (x - 1) (x - 2) (x + 5)$ must be changing its sign are $x = - 5, 1, 2$ .
Therefore, $f (x) < 0$ for $x < - 5$ and $1 < x < 2$ .
Hence, option 'B' is correct.

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