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

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Answer 1 · 2016-07-19T21:23:01

$- 13 \times - 12 = 156$ $-13 xx -12 = 156$

Let the two integers be $x and x + 1$ $x and x+1$

Their product will be positive.

$x \times (x + 1) = 156$ $x xx (x+1) = 156" "$ this leads to a quadratic equation.

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

We need factors of 156 which differ by 1.

They will need to be very close to $\sqrt{156}$ $sqrt156$ , so lets start there.
$\sqrt{156} = 12.4899$ $sqrt 156 = 12.4899$

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

$(x + 13) (x - 12) = 0$ $(x +13)(x-12) = 0$

$x = - 13 or x = 12$ $x = -13 or x = 12" "$ reject 12 as we are looking for negative integers.

The integers are -13 and -12.