Question

Set of values of x satisfying the inequality `((x - 3)^2(2x + 5)(x - 7))/((x^2 + x + 1)(3x - 6)^2)` ≤ 0 is [a, b) ∪ (b, c] then 2a + b + c is equal to ______.

पर्याय

• 0

• 4

• 5

• 7

Answer 1

Set of values of x satisfying the inequality `((x - 3)^2(2x + 5)(x - 7))/((x^2 + x + 1)(3x - 6)^2)` ≤ 0 is [a, b) ∪ (b, c] then 2a + b + c is equal to 4.

Explanation:

x² + x + 1 > 0;

3x – 6 ≠ 0

x ≠ 2

Put (x – 3) = 0

⇒ x = 3

So the inequality becomes (2x + 5)(x – 7) ≤ 0

`x∈[-5/2,7]`

But x ≠ 2

So `x∈[-5/2, 2) ∪ (2, 7]`

a = `-5/2`, b = 2, c = 7

2a + b + c = 4