What will be the sign of the product of 8 negative and 11 positive integers ​

Question

What will be the sign of the product of 8 negative and 11 positive integers

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Kennedy 1 month 2021-08-15T08:47:22+00:00 2 Answers 0 views 0

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    0
    2021-08-15T08:48:33+00:00

    The answer is negative. Odd numbers of negative integers when multiplied yield negative integer only. Consider an integer -x = (-1)*x. Let -y be another integer.

    Then product of -x * -y = (-1)^2* xy = xy

    similarly – x* -y* -z = (-1)^3* xyz = -xyz

    -x*-y*-z*-s = (-1)^4* xyzs = xyzs

    proceeding same way, you will observe that multiple of odd negative numbers are resulting in negative digit while multiples of even negative numbers will result in positive digits. A digit when multiplied by positive numbers, the sign of the resultant digit wont change. Hence the answer should be a positive.

    0
    2021-08-15T08:49:04+00:00

    positive sign will be there because the negatives are in even no. and if they are in even quantity then positive sign remains

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