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Answer :
Final answer:
To find the lesser integer, we solve the quadratic equation x(x+1) = 600 by factoring it into (x+25)(x-24) = 0 and determine the value of x.
Explanation:
Let's assume the first integer as x. The next consecutive negative integer will be x+1. We know that the product of these two integers is 600. So, we can write the equation as x(x+1) = 600.
Expanding this equation, we get x^2 + x - 600 = 0. Now, let's factorize this quadratic equation to find the values of x.
Factoring, we can rewrite the equation as (x+25)(x-24) = 0. So, the possible values of x are -25 and 24. Since we were asked for the lesser integer, the value of the lesser integer is -25.
Learn more about Solving quadratic equations here:
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