The correct option is B 4 and 3
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Let the required number be x.
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Then, the number obtained by decreasing it by 7 is given byx−7.
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Given, the product of these two numbers is -12.
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⇒x(x−7) = −12
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⇒x2−7x = −12
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⇒x2−7x+12 = 0
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The roots of a quadratic equation ax2+bx+c=0, where a,b and c are constants (a≠0) are given by
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x=−b±√b2−4ac2a.
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Since a=1,b=−7 and c=12, we have
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x=7±√(−7)2−4× 1× 122× 1.
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⟹x=4,3
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Thus, 3 and 4 are the roots of the given quadratic equation.
Therefore, the possible values of the number are 3 and 4.