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Solving Quadratic Inequations
What is to be learned?
• The best tactic for solving quadratic inequations
Solving Quadratic Equations
Solve x2 – 2x – 8 = 0Factorise
(x – 4)(x + 2) = 0 x = 4 or x = -2
Big Nasty FormulaBig LTrial and ErrorTry x = 2 22 – 2(2) – 8 = -8 Try x = 4 42 – 2(4) – 8 = 0
22
Solving Quadratic Equations
Solve x2 – 2x – 8 = 0Graphically
y = xy = x22 – 2x – 8 – 2x – 8
-2-2 44-4-4
xx22 – 2x – 8 = 0 – 2x – 8 = 0
x = -2 or 4x = -2 or 4
very easy very easy ififyou have a graphyou have a graph
Graphically is the way to goSolve x2 + 2x – 15 < 0Need graph y = xy = x22 + 2x – 15 + 2x – 15
Find RootsFind Roots Factorise Factorise(x + 5)(x – 3)(x + 5)(x – 3)
roots x=-5 or 3roots x=-5 or 3
Solving Quadratic Inequations
33
Solving Quadratic InequationsSolve x2 + 2x – 15 < 0Roots x = -5 or 3
-5-5
xx22 + 2x – 15 < 0 + 2x – 15 < 0y = xy = x22 + 2x – 15 + 2x – 15
y positivey positive
y negativey negative
Solving Quadratic InequationsSolve x2 + 2x – 15 < 0Roots x = -5 or 3
-5-5
xx22 + 2x – 15 < 0 + 2x – 15 < 0xx is between -5 and 3 is between -5 and 3y = xy = x22 + 2x – 15 + 2x – 15
y positivey positive
y negativey negative
-5 < x < 3-5 < x < 3
33
Solving Quadratic Inequations
Best done by drawing a graphFor graph, needFor roots
rootsrootsFactoriseFactorise
Solve x2 + x – 6 > 0Need graph y = xy = x22 + x – 6 + x – 6
Find RootsFind Roots Factorise Factorise(x + 3)(x – 2)(x + 3)(x – 2)
roots x= -3 or 2roots x= -3 or 2
22
Solve x2 + x – 6 > 0Roots x = -3 or 2
-3-3
xx22 + x – 6 > 0 + x – 6 > 0y = xy = x22 + x – 6 + x – 6
y positivey positive
y negativey negative
22
Solve x2 + x – 6 > 0Roots x = -3 or 2
-3-3
xx22 + x – 6 > 0 + x – 6 > 0y = xy = x22 + x – 6 + x – 6
y positivey positive
y negativey negativex < -3x < -3 and x > 2and x > 2
Solve:1.x2 – 5x + 6 < 0 2.x2 – 2x – 8 > 0 3.x2 – 16 < 04.x2 – 10x > 05.10x – x2 > 0 6.x2 – 3x – 18 ≥ 07.2x2 – 8x + 6 ≤ 0 8.x2 + 8x + 16 < 0 9.x2 + 8x + 16 ≤ 0 10. x2 + 8x + 16 > 0 .
2 < x < 32 < x < 3
x > 4 or x < -2 x > 4 or x < -2 Key QuestionKey Question
x > 10 or x < 0 x > 10 or x < 0 0 < x < 100 < x < 10
x x ≥ 6 or x 6 or x ≤ -2 -2 1 1 ≤ x x ≤ 33
x2 – 16 < 0Factorising (x – 4)(x + 4) Roots x = 4 and x = -4
Key QuestionKey Question
44-4-4
-4 < x < 4-4 < x < 4
