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For how many integer values does the following inequality hold good? (x + 2) (x + 4) (x + 6)........(x + 100) < 0?
A. 25 B. 50 C. 49 D. 47
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There are 50 critical value of the given function i.e. x = {-2, -4, -6.......-100}
CONCEPT: Critical Values are the values of x for which function becomes zero
Graph between any two critical values holds the same sign and the sign of function changes right after critical values
Since graph will result in a positive value for x > -2 i.e. NOT ACCEPTABLE REGION therefore Graph will be negative between -4 < x < -2 i.e. 1 values Graph will be Positive between -6 < x < -4 i.e. NOT ACCEPTABLE REGION Graph will be negative between -8 < x < -6 i.e. 1 values Graph will be Positive between -10 < x < -8 i.e. NOT ACCEPTABLE REGION Graph will be negative between -12 < x < -10 i.e. 1 values Graph will be Positive between -14 < x < -12 i.e. NOT ACCEPTABLE REGION Graph will be negative between -16 < x < -14 i.e. 1 values and so on....
So out of 50 there will be 25 values of x for which graph will be Negative
Answer: Option A
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