Question

The roots of x^2-999999x-9999=0 and ? are additive intergers

A. x^2+999999x-9999=0
B. x^2-999999x+9999=0
C. x^2+999999x+9999=0
D. x^2-9999x-999999=0

Answer 1

Don't quote me on this, but my logic in picking an answer (if you meant inverses instead of integers in your question) is that the equation's roots are a positive and a negative, thte negative having a larger absolute value. This can be seen by the fact that positive times negative yields a negative product, and the third term is negative. But the second term is also negative, so the negative root must have the larger magnitude. So for the roots of another equation to be additive inverses, it would have to have the same roots with the only difference being that the negative and positive would switch values. Therefore the answer seems to be (I'm not actually telling you the answer); the third term is still negative, so the roots are of opposite signs. But this time the second term is positive, therefore the positive root has the greater absolute value.