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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.5

Question 1.

Solve 2x^{2} + x – 15 ≤ 0.

Solution:

To find the solution of the inequality

ax^{2} + bx + c ≥ 0 or ax^{2} + bx +c ≤ 0 (for a > 0)

First we have to solve the quadratic equation ax^{2} + bx + c = 0

Let the roots be a and P (where a < P)

So for the inequality ax^{2} + bx + c ≥ 0 the roots lie outside α and β

(i.e.,) x ≤ α and x ≥ β

So for the inequality ax^{2} + bx + c ≤ 0. The roots lie between α and β

(i.e.,) x > α and x < β (i.e.) a ≤ x ≤ β

Question 2.

Solve -x^{2} + 3x – 2 ≥ 0

Solution:

-x^{2} + 3x – 2 ≥ 0 ⇒ x^{2} – 3x + 2 ≤ 0

(x – 1) (x – 2) ≤ 0

[(x – 1) (x – 2) = 0 ⇒ x = 1 or 2. Here α = 1 and β = 2. Note that α < β]

So for the inequality (x – 1) (x – 2) ≤ 2

x lies between 1 and 2

(i.e.) x ≥ 1 and x ≤ 2 or x ∈ [1, 2] or 1 ≤ x ≤ 2

### Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.5 Additional Questions

Question 1.

Solve for x.

Solution:

Select the intervals in which (3x +1) (3x – 2) is positive

(3x + 1) > 0 and (3x – 2) > 0 or

3x +1 < 0 and 3x – 2 < 0

Question 2.

Solution:

Question 3.

Solution: