SOLUTION: The roots of the equation x^2+2px+q differ by 1.show that p^2=q+1/4

SOLUTION: The roots of the equation x^2+2px+q differ by 1.show that p^2=q+1/4

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Question 1199514: The roots of the equation x^2+2px+q differ by 1.show that p^2=q+1/4

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Using the quadratic formula, the two roots are (-2p + sqrt(4p^2-4q))/2 and
(-2p - sqrt(4p^2-4q))/2. Simplifying and setting the difference equal to 1 we get:
-p + sqrt(p^2-q) - (-p - sqrt(p^2-q)) = 1
2*sqrt(p^2-q) = 1 -> p^2-q = 1/4
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