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Question

If b>a, then the equation (x-a)(x-b)-1=0, has:


Solution

The given quadratic equation is:
(x-a)(x-b)-1=0
Let f(x) = (x-a) (x-b)-1
f(a) = -1 and f(b) = -1
f(a) = f(b) and f(a) < 0 and f(b) < 0
coefficient of x2=1
therefore the curve f(x) is opening upwards parabola and a and b lies between the roots.
Therefor e one root lies in the interval (,a) and other root lies in the interval (b,).


 

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