SOLUTION: Given that x^2+px+q and 3x^2+q have a common factor x-b, where p,q and b are non-zero, show that 3p^2+4q=0.

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Question 1035463: Given that x^2+px+q and 3x^2+q have a common factor x-b, where p,q and b are non-zero, show that 3p^2+4q=0.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Putting in the text here is difficult. Follow this described process, so far still incomplete:

First expression divided by x-b should have remainder of 0, equal to pb%2Bb%5E2%2Bq.

Second expression divided by x-b should have also remainder of 0, equal to 3b%5E2%2Bq.

You would do those with polynomial division OR synthetic division. Your choice.

You can equate the two expressions found for the remainder since both are 0.
pb%2Bb%5E2%2Bq=3b%5E2%2Bq
will give you ..... b%282-p%29=0
from which you pick that highlight%28p=2%29------so you have some part of the solution, but not yet the entire solution.

Next, look at the two equations for the remainders.