Question

solve the following equation

(x-3)(x+1)(x-2)(x-9)>=0​

Answer 1

EXPLANATION.

Equation.

⇒ (x - 3)(x + 1)(x - 2)(x - 9) > 0.

As we know that,

First we find the zeroes of the equation, we get.

⇒ x - 3 = 0.

⇒ x = 3. - - - - - (1).

⇒ x + 1 = 0.

⇒ x = -1. - - - - - (2).

⇒ x - 2 = 0.

⇒ x = 2. - - - - - (3).

⇒ x - 9 = 0.

⇒ x = 9. - - - - - (4).

All the zeroes of the equation we can put it on wavy curve method, we get.

x ∈ (-∞,-1) ∪ (2,3) ∪ (9,∞).

                                                                                                                       

MORE INFORMATION.

Inverse of a relation.

Let A, B be two sets and let R be a relation from set A to B. Then the inverse of R, denoted by R⁻¹, is a relation from B to A and is defined by R⁻¹ = {(b, a) : (a, b) ∈ R}, Clearly,

(a, b) ∈ R ⇔ (b, a) ∈ R⁻¹ Also,

Domain of R = Range of R⁻¹ and,

Range of R = Domain of R⁻¹.