Question

If alpha is less than beta then x minus alpha × xminus beta greater than or equal to 0 is

Answer 1

Answer:

greater than zero

Step-by-step explanation:

because of alpha less than beta.

there x is constant term .

so (x-alpha)(x-beta)is greater than zero

Answer 2

Answer:

The given equation will be greater than zero when x ∈ (-∞, α) ∪ (β, ∞).

and less than zero when x ∈ (α, β).

Step-by-step explanation:

Given,

alpha (α) is less than beta(β)

or, α < β

Then, (x - α) * ( x -β) will be:

Let's assume Y = (x - α) * ( x -β)----------------------------------(1)

Y = x² - (α+β)x +αβ

Since α and β are two distinct roots of eq(1), it will represent a parabola in the cartesian plane.

Also, the eq(1) will be greater than zero when x ∈ (-∞, α) ∪ (β, ∞).

and less than zero when x ∈ (α, β).