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In the quadratic equation
x^2 + mx + 2=0, the roots are
consecutive. Find the values of m .
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Your formulation is fatally uncompleted. The correct and the complete formulation is THIS:
In the quadratic equation x^2 + mx + 2=0, the roots are consecutive integer numbers. Find the values of m .
Solution
From Vieta's theorem, the constant term "2" is the product of the roots that are two consecutive integer numbers.
Hence, the roots are EITHER 1 and 2 with m equal to -(1+2) = -3
OR -2 and -1 with m equal to -((-1) + (-2)) = 3.
Answer. The problem has two solutions: a) the roots 1 and 2 with m = -3, and
b) the roots are -2 and -1 with m= 3.
Solved.
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The solution by @josgarithmetic was uncompleted.
What he presents as a solution, is not a solution at all.
It is a RUBBISH. Simply ignore it for your safety. It makes no sense.
Avoid his writing and his "solutions" as much as you can.
You will learn NOTHING from him.