the product of two consecutive negative integers is 600. what is the value of the lesser integer? -60 -30…

Explanation:

Step1: Let the two consecutive negative integers

Let the first (lesser) negative - integer be (x), then the next consecutive negative integer is (x + 1).

Step2: Set up the equation

Since their product is 600, we have the equation (x(x + 1)=600), which expands to (x^{2}+x - 600=0).

Step3: Factor the quadratic equation

We factor (x^{2}+x - 600) as ((x + 25)(x - 24)=0).

Step4: Solve for (x)

Setting each factor equal to zero gives (x+25 = 0) or (x - 24=0). So (x=-25) or (x = 24). But we are looking for negative integers, so we discard (x = 24).

Answer:

C. -25