For the equation x^2 + dx + g = 0, d and g are integers. The only possible value of x is 4. What is the value of d?
Question comes from John in Kentucky.
This one involves some algebra skills and good logic. So where to begin?
Well, you may want to try substituting the 4 in for x. While this usually is a good tactic, you will find that it does not help much here. You are still left with two variables and are unable to come to a single answer for the value of d.
Now if you think you are stumped, remember a line from The Black Book - Think "What can I do here?". Think about this sort of problem - you have probably seen plenty of problems of the form Ax^2 + Bx + C = 0. What do you usually do with them? - break them into (x+__) (x+__)=0
Back to the problem, we see x can only = 4, this means the problem must break down into
(x-4) (x-4) = 0
so, FOILed out it would look like x^2 - 8x + 16
look back to the question, your answer is...... d = -8
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