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