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Question

The product of a number and the one obtained by decreasing it by 7 is -12. Then, the possible values for the number are .

A
-3 and -4
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B
4 and 3
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C
-3 and 2
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D
2 and -4
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Solution

The correct option is B 4 and 3
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Let the required number be x.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Then, the number obtained by decreasing it by 7 is given byx7.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Given, the product of these two numbers is -12.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x(x7) = 12
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x27x = 12
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x27x+12 = 0
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> The roots of a quadratic equation ax2+bx+c=0, where a,b and c are constants (a0) are given by
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x=b±b24ac2a.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Since a=1,b=7 and c=12, we have
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x=7±(7)24× 1× 122× 1.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> x=4,3
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Thus, 3 and 4 are the roots of the given quadratic equation.
Therefore, the possible values of the number are 3 and 4.

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