Question

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

A
both roots in [a,b]
B
both roots in (,a)
C
both roots in (b,)
D
one root in (,a) and other in (b,)

Solution

## The correct option is D one root in $$\left( -\infty ,a \right)$$ and other in $$\left( b,\infty \right)$$Let $$f(x)=(x-a)(x-b)-1$$$$f(a)=-1$$    which is negative.$$f(b)=-1$$   this is also negative.Therefore, roots do not lie between $$a$$ and $$b$$.Thus, one root in $$(-\infty ,a)$$ and other root lies in $$(b,\infty )$$.Hence, option 'D' is correct.Mathematics

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