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# The product of two consecutive negative integers is 600. What is the value of the lesser integer?

**Solution:**

Given: Product of two consecutive negative integers is 600

Let ‘x’ and ‘(x + 1)’ be the required negative integers such that,

⇒ x(x + 1) = 600

x^{2} + x = 600

x^{2} + x - 600 = 0

By splitting the terms of this quadratic equation, we get

x^{2 }+ 25x - 24x - 600 = 0

x(x + 25) - 24(x + 25) = 0

(x - 24)(x + 25) = 0

(x - 24) = 0 ⇒ x = 24

This is not possible given that integers are negative.

(x + 25) = 0 ⇒ x = -25

Required integers are -25 and -24.

The value of the smallest integer is -25.

## The product of two consecutive negative integers is 600. What is the value of the lesser integer?

**Summary:**

The product of two consecutive negative integers -25 and -24 is 600. The value of the lesser integer is -25.

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