Theory of Equations 4 Question 5
6. If $b>a$, then the equation $(x-a)(x-b)-1=0$ has
(a) both roots in $(a, b)$
(2000, 1M)
(b) both roots in $(-\infty, a)$
(c) both roots in $(b,+\infty)$
(d) one root in $(-\infty, a)$ and the other in $(b, \infty)$
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Solution:
From graph, it is clear that one of the roots of $(x-a)(x-b)-1=0$ lies in $(-\infty, a)$ and other lies in $(b, \infty)$.
