If x a set of all real numbers R the find the solution set for $(x - 3) (x + 5) < 0$

$[3, \infty)$

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$(- 5, 3)$

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$[- 5, \infty)$

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$[- 5, 3]$

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Solution

The correct option is B
$(- 5, 3)$

Case 1 :
When (x-3) > 0 and (x+5) <0
i.e. x > 3 and x < -5
This is not possible as as a number greater than 3 cannot be less than -5

Case 2:
When (x-3) < 0 and (x+5) > 0
i.e. x < 3 and x > -5
-5 < x < 3, which is possible.
Therefore Solution set = $(- 5, 3)$

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If x a set of all real numbers R the find the solution set for (x−3)(x+5)<0

The correct option is B (−5,3) Case 1 : When (x-3) > 0 and (x+5) <0 i.e. x > 3 and x < -5 This is not possible as as a number greater than 3 cannot be less than -5 Case 2: When (x-3) < 0 and (x+5) > 0 i.e. x < 3 and x > -5 -5 < x < 3, which is possible. Therefore Solution set = (−5,3)

If x a set of all real numbers R the find the solution set for $(x - 3) (x + 5) < 0$

The correct option is B
$(- 5, 3)$

Case 1 :
When (x-3) > 0 and (x+5) <0
i.e. x > 3 and x < -5
This is not possible as as a number greater than 3 cannot be less than -5

Case 2:
When (x-3) < 0 and (x+5) > 0
i.e. x < 3 and x > -5
-5 < x < 3, which is possible.
Therefore Solution set = $(- 5, 3)$