Solve the in equation 2 - 3 x - 2 x 2 ≥ 0 by algebraic method.

Given, 2 - 3 x - 2 x 2 ≥ 0 Multiplying both sides by - 1 we get 2 x 2 + 3 x - 2 ≤ 0 ⇒ 2 x 2 + 4 x - x - 2 ≤ 0 ⇒ 2 x 2 + 4 x - x - 2 ≤ 0 ⇒ 2 x ( x + 2 ) - 1 ( x + 2 ) ≤ 0 ⇒ ( 2 x - 1 ) ( x + 2 ) ≤ 0 ⇒ - 2 ≤ x ≤ 1 2

Solve the in equation x 2 - 4 x - 21 ≥ 0 by algebraic method.

Given, x 2 - 4 x - 21 ≥ 0 ⇒ x 2 - 7 x + 3 x - 21 ≥ 0 ⇒ x x - 7 + 3 x - 7 ≥ 0 ⇒ x - 7 x + 3 ≥ 0 ⇒ x ⩾ 7 ∪ x ⩽ - 3

Solve the in equation 15 x 2 + 4 x - 4 ≤ 0 by graphical method.

Given, 15 x 2 + 4 x - 4 ≤ 0 ⇒ 15 x 2 + 10 x - 6 x - 4 ≤ 0 ⇒ 5 x ( 3 x + 2 ) - 2 ( 3 x + 2 ) ≤ 0 ⇒ - 2 3 ≤ x ≤ 2 5

Solve the in equation x 2 - 4 x - 21 ≥ 0 by graphical method.

Given, x 2 - 4 x - 21 ≥ 0 Let, y = x 2 - 4 x - 21 ⇒ y = x 2 - 7 x + 3 x - 21 ⇒ y = ( x - 7 ) ( x - 3 ) x 0 1 2 3 4 5 6 7 8 y 21 12 5 0 - 3 - 4 - 3 0 5 From the graph, we can see that y ≥ 0 for x ≤ 3 and x ≥ 7 ∴ Solution of x 2 - 4 x - 21 ≥ 0 is ( - ∞ , 3 ] ∪ [ 7 , ∞ ) .

Solve the in equation 3 x - 8 < - 2 .

Given, 3 x - 8 < - 2 We know that 3 x - 8 > 0 ⇒ x > 8 3 Also 3 x - 8 ≥ 0 ∴ Solution does not exist.

Solve the in equation - x 2 + 6 x - 5 > 8 - 2 x .

Given, - x 2 + 6 x - 5 > 8 - 2 x ...(i) ⇒ - x 2 + 6 x - 5 ≥ 0 ⇒ x 2 - 6 x + 5 ≤ 0 ⇒ ( x - 5 ) ( x - 1 ) ≤ 0 ⇒ 1 ≤ x ≤ 5 ...(ii) Squaring (i) on both sides, we get - x 2 + 6 x - 5 > 64 + 4 x 2 - 32 x ⇒ 0 > 5 x 2 - 38 x + 64 + 5 ⇒ 5 x 2 - 38 x + 69 < 0 ⇒ 5 x 2 - 23 x - 15 x + 69 < 0 ⇒ 5 x ( x - 3 ) - 23 ( x - 3 ) < 0 ⇒ ( x - 3 ) ( 5 x - 23 ) < 0 ⇒ 3 < x < 23 5 ...(iii) Intersection of (ii) and (iii) is 3 < x < 23 5 .

E M B I B E

Intermediate Second Year Mathematics Paper 2A>Algebra>Chapter 3 - Quadratic Expressions>Exercise 3(c)

Telangana Board Solutions for Exercise 3: Exercise 3(c)

Author:Telangana Board

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Exercise 3: Exercise 3(c)

Attempt the free practice questions from Exercise 3: Exercise 3(c) with hints and solutions to strengthen your understanding. Intermediate Second Year Mathematics Paper 2A solutions are prepared by Experienced Embibe Experts.