Question

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

Answer 1

Answer:

Value of lesser integer is -25

Step-by-step explanation:

Let the two consecutive negative integers be $x , x+1$ .

Given: Product of two consecutive negative integers is 600

$x(x+1)=600$

using property (multiplication is distributive over addition): $a(b+c) = ab+ac$ , we get

$x(x+1)=600\\x^2+x=600\\x^2+x-600=0\\x^2+25x-24x-600=0\\x(x+25)-24(x+25)=0\\(x-24)(x+25)=0\\x=24\,\,-25$

As x is negative, $x=24$ is rejected

Therefore, $x=-25$

So, $x+1=-25+1=-24$

We know that $24< 25$ . On multiplying both sides by -1, we get

$-25< -24$

So, value of lesser integer is -25

Answer 2

-24*-25 = 600
-24<-25
hence answer is -24