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 the other in (b, +∞)

Answer 1

Answer: (D)

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

Answer 2

The given equation is (x – a)(x – b) – 1 = 0, b > a

Or x² – (a + b) x + ab – 1 = 0

Since coeff. of x² i.e. 1 > 0 ∴ it represents upward parabola, intersecting x axis at two points. (corresponding to two real roots, D being +ve)

Also f (1) = f (2) = - 1 ⇒ curve is below x-axis at a and b ⇒ a

and b both lie between the roots.

Thus the graph of given eqⁿ is as shown.

From graph it is clear that one root of the equation lies in

(- ∞, a) and other in (b, ∞).