Quadratic EquationHard
Question
The equation $(x - a)(x - a - b) = 1$, where $a,b$ are positive constants has
Options
A.One root less than a and the other is greater than a.
B.One root less than $a + b$ and the other is greater than $a + b$.
C.One root less than a and the other is greater than $a + b$.
D.Roots lying between a and $a + b$.
Solution
$f(x) = (x - a)(x - a - b) - 1$
$$f(a) = f(a + b) = - 1 $$From graph it is clear that
root lie in internal $( - \infty,a) \cup (a + b,\infty)$
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