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Least Integer Function

If -3 < x <...

Question

If $- 3 < x < 1$ , then the value of $3 - 2 x - x^{2}$ is:

A

Zero

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B

Positive

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C

Negative

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D

Cannot be determined

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Solution

The correct option is B Positive
Let
$f (x) = - x^{2} - 2 x + 3$
$= - (x^{2} + 2 x - 3)$
$= - (x + 3) (x - 1)$
$= (x + 3) (1 - x)$
If $f (x) > 0$
Therefore
$(x + 3) (1 - x) > 0$
Which implies
$x > - 3$ , $x < 1$
Therefore $- 3 < x < 1$
Hence $f (x)$ is positive in the given interval of $x$
Answer is B

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