SOLUTION: <img src="http://img338.imageshack.us/img338/9167/mathaq6.png"> I NEED HELP! :]

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Question 117516:
I NEED HELP! :]
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


Solve for d

Plug in into


Group like terms


Factor out the GCF from each individual group


Factor by using the difference of cubes formula to get


Factor by using the difference of squares formula to get


Notice how we have the common term . We can factor this term out.


Factor out the GCF


Now if we let and we'll get




So by the zero product property we get

or


but since , this means



Now solve for x





So is a zero of if the coefficients satisfy the equation



-------------------------------------
Check:

Unfortunately, there is no formal check for this type of problem. But if we make sure that the coefficients satisfy the equation , then we can graph the equation and see that one root is . For instance, let and so we'll get


(notice how which satisfies the equation )


Now graph the polynomial to get





and we can see that one root is


If we try different values of a,b,c, and d that will satisfy the equation , we'll see that is a root every time. So in a way, our answer has been verified.
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