Solving Quadratic Inequalities Algebraically

 Solving Quadratic Inequalities Algebraically

 

Education The quadratic inequalities are to replace the in-equal symbol with an equal symbol and then solve the resultant equations. The result for the equations allows establishing the given interval for the inequality. Select any one of the number from each interval and to check for their originality. If the number from that interval is true and then that interval is the resultant interval is the solution for the inequality. The example for the quadratic inequalities are x^2+17 x+19greater than 0. Examples for the solving quadratic inequalities algebraically: Example 1 for solving quadratic inequalities algebraically: Solve the quadratic inequality equation x^2 -x- 42 greater than0 Solution: The given quadratic inequality equation is x^2 -x- 42 greater than0 The given equation is in the inequality equation. So replace the in- equal symbol as the equal symbol. Find the solution for the equality equation. x^2 -x- 42 greater than0 is converted into x^2 -x- 42 =0. Find the factors for that equation. x^2 -x -42= x^2- 7x+ 6x- 42 x^2 -x -42= x^2-7x+ 6x-(7 x 6) Take x as common in first two terms and take 6 as common in the next two terms. x^2 –x -42= x(x- 7) + 6(x-7) Take x- 7 as the common term in the above equation to

 get two roots. x^2 –x -42=(x-7) (x+6) Equate x-7 and x+6 to 0 to get the roots for the given equation. x- 7=0 and x+6 =0 In first equation add by 7 on both sides of the equation. In the second equation subtract by 6 on both sides of the equation. x- 7 +7 =0+7 and x+6 -6=0-6 x= 7 and x= -6 The roots for the equation x^2 –x -42=0 are x=7 and x=-6. So the solution for the inequality equation x^2 –x- 42 greater than0 is xgreater than 7 and xless than -6. Example 2 for solving quadratic inequalities algebraically: Solve the equation x^2 -2x- 35 greater than0 Solution: The given quadratic inequality equation is x^2 -2x- 35 greater than0 The given equation is in the inequality equation. So replace the in- equal symbol as the equal symbol. Find the solution for the equality equation. x^2 -2x- 35 greater than0 is converted into x^2 -2x- 35 =0. Find the factors for that equation. x^2 -2x- 35 = x^2- 7x+ 5x- 35 x^2 -2x- 35 = x^2-7x+ 5x-(7 x 5) Take x as common in first two terms and take 5 as common in the next

 two terms. x^2 -2x- 35 = x(x- 7) + 5(x-7) Take x- 7 as the common term in the above equation to get two roots. x^2 -2x- 35 =(x-7) (x+5) Equate x-7 and x+5 to 0 to get the roots for the given equation. x- 7=0 and x+5 =0 In first equation add by 7 on both sides of the equation. In the second equation subtract by 5 on both sides of the equation. x- 7 +7 =0+7 and x+5 -5=0-5 x= 7 and x= -5 The roots for the equation x^2 -2x- 35 =0 are x=7 and x=-5. So the solution for the inequality equation x^2 -2x- 35 greater than0 is xgreater than 7 and xless than -5. Practice problem for solving quadratic inequalities algebraically: Solve the quadratic equation x^2- 3x-18greater than0 Answer: xgreater than 3 and xless than -6. Learn more on about spherical triangles and its Examples. Between, if you have problem on these topics decimal point values, keep checking my articles i will try to help you. Please share your comments.