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Question

The quadratic equation,  $${x}^{2}+ax+12$$ can be factorised , where one of the roots $$k$$, is a negative integer. Then the possible value of $$k$$ is?


A
13
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B
12
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C
6
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D
7
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Solution

The correct options are
B $$-12$$
C $$-6$$
Since the above equation has real roots and the product of the roots is positive, hence either both the roots are positive or both the roots are negative. However, it is given that one of the root is negative, hence both the roots are negative. Therefore the possible roots are $$(\pm1,\pm12),(\pm2,\pm6),(\pm3,\pm4)$$.

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