# How do you find two consecutive, negative integers whose product is 156?

Jul 19, 2016

$- 13 \times - 12 = 156$

#### Explanation:

Let the two integers be $x \mathmr{and} x + 1$

Their product will be positive.

$x \times \left(x + 1\right) = 156 \text{ }$ this leads to a quadratic equation.

${x}^{2} + x - 156 = 0$

We need factors of 156 which differ by 1.

They will need to be very close to $\sqrt{156}$, so lets start there.
$\sqrt{156} = 12.4899$

$12 \times 13 = 156$ which gives us exactly what we want.

$\left(x + 13\right) \left(x - 12\right) = 0$

$x = - 13 \mathmr{and} x = 12 \text{ }$ reject 12 as we are looking for negative integers.

The integers are -13 and -12.