Question

How to define Wavy Curve Method f(x)?

(a) (x-a1)^n1 / (x-a2)^n2 / (x-a3)^n3 …………… / (x-ak)^nk * (x-b1)^m1 / (x-b2)^m2 / (x-b3)^m3 …….. /(x-bp)^mp

(b) (x-a1)^n1 + (x-a2)^n2 +(x-a3)^n3 …………… + (x-ak)^nk / (x-b1)^m1 + (x-b2)^m2 + (x-b3)^m3 …….. + (x-bp)^mp

(c) (x-a1)^n1 (x-a2)^n2 (x-a3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp

(d) (x-a1)^n1 – (x-a2)^n2 – (x-a3)^n3 …………… – (x-ak)^nk / (x-b1)^m1 – (x-b2)^m2 – (x-b3)^m3 ……..- (x-bp)^mp

I had been asked this question during a job interview.

I'm obligated to ask this question of Sets and their Representations in chapter Sets of Mathematics – Class 11

Answer 1

The correct answer is (c) (x-a1)^n1 (x-a2)^n2 (x-a3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp

The best explanation: The method of intervals {or wavy curve} is used for solving inequalities of the form

f(x) = (x-a1)^n1 (x-a2)^n2 (x-a3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp > 0 (< 0, ≤ 0, or ≥ 0)

 where, n1, n2, ,n3, …….. nk and m1, m2, m3, …….. , mp are natural numbers .

 a1, a2, a3, ……..ak and b1, b2, b3, …….. bp are any real numbers such that ai ≠ bj where i = 1, 2, 3, ……. , k and j = 1, 2, 3, ….. , p.