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, +∞)

Answer 1

Answer: (D)

One root in (– ∞, a) and other in (b, +∞)

Answer 2

We have, $(x - a)(x - b) - 1 = 0$

$(x - a)(x - b) = 1 > 0$ ⇒ $(x - a)(x - b) > 0$ [∵ b > a]

$x \in \rbrack - \infty,a\lbrack \cup \rbrack b, + \infty\lbrack$ , i.e. $( - \infty,a)$ and (b, ∞).