If the equation
x^2 + ax + b = 0 and x^2 + px + q = 0 have a common root,
prove that (a - p)(bp - aq) = (b - q)^2
P.S. Not Homework!!!!!!!!!!
AMaths(2) - Quadratic Equation
2010-09-04 4:22 am
回答 (1)
2010-09-04 4:44 am
✔ 最佳答案
Let @ be the common root.Then @^2 + a@ + b = 0 .....(1)
and
@^2 + p@ + q = 0 .....(2)(1) - (2) :(a - p)@ + b - q = 0@ = (q - b) / (a - p) .....(3)
(1) * p - (2) * a :(p - a)@^2 + bp - qa = 0@^2 = (qa - bp) / (p - a) .....(4)
(3)^2 = (4) :[(q - b)^2] / (a - p)^2] = (qa - bp) / (p - a)i.e.(a - p)(bp - aq) = (b - q)^2
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