Question

The product of two consecutive integer is $12$. What is the second integer?

• A. $4$ or $-1$
• B. $4$ or $-3$
• C. $3$ or $-3$
• D. $2$ or $-3$

Answer 1

Answer: (B)

$4$ or $-3$

Let the two consecutive numbers be $x$ and $x+1$
Therefore, product of two consecutive number $=x(x+1)=12$
$⟹x^2+x=12$

$⟹x^2+x-12=0$

$⟹x^2+4x-3x-12=0$

$⟹x(x+4)-3(x+4)=0$

$⟹(x-3)(x+4)=0$

$⟹x-3=0$ or $x+4=0$
we get, the value of $x=3$ or $-4$
So, the second number will be $4$ or $-3$.