SOLUTION: Suppose the roots of an equation 2x²+3px+5q differ by 1,find the equation connecting p and q

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Question 1015811: Suppose the roots of an equation 2x²+3px+5q differ by 1,find the equation connecting p and q
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Suppose the roots of an equation 2x²+3px+5q differ by 1,find the equation connecting p and q
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Actually, there is no equation here.
You missed the sign "=" and the right side.


But if it is 2x%5E2+%2B+3px+%2B+5q = 0, then the roots are 

x%5B1%5D = %28-3p+%2B+sqrt%289p%5E2-4%2A2%2A5q%29%29%2F4, 

x%5B2%5D = %28-3p+-+sqrt%289p%5E2-4%2A2%2A5q%29%29%2F4.

The difference  x%5B1%5D - x%5B2%5D (in this order) is 

%282%2Asqrt%289p%5E2+-+40q%29%29%2F4 = %28sqrt%289p%5E2+-+40q%29%29%2F2.

It is equal to 1 (or -1):

%28sqrt%289p%5E2+-+40q%29%29%2F2 = +/-1.

Square both sides:

(9p^2 - 40q)/4 = 1,   or   9p^2 - 40q = 4.

It is your equation for p and q.