SOLUTION: write an equation in the form ax^2+bx+c=0 given one root of 5+i

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Question 385897: write an equation in the form ax^2+bx+c=0 given one root of 5+i
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Divide both sides by a: x%5E2+%2B+bx%2Fa+%2B+c%2Fa+=+0. If one root is 5+i then 5 - i is also a root. Then -b%2Fa+=+5%2Bi+%2B+5+-+i+=+10, or b = -10a. Also, c%2Fa+=+%285%2Bi%29%285+-+i%29+=+25+-i%5E2+=+26, or c = 26a. Therefore ax%5E2%2Bbx%2Bc=ax%5E2+-+10ax+%2B+26a+=+0, or x%5E2+-+10x+%2B+26+=+0, after dividing by a.