Inequalities with Quadratic Functions

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Inequalities with Quadratic Functions

• Solving inequality problems

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Quadratic inequalities
means for what values of x is this quadratic
above the x axis
ax2bxcgt0
e.g. x2 x - 20 gt0
means for what values of x is this quadratic
below the x axis
ax2bxclt0
e.g. x2 x - 20 lt 0
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Pg 75 Q3
Inequality Problems (1)
n(n1) 2
The nth triangular number is given by
A) Find the value of n that gives the first
triangular number over 100
B) What is the first triangular number over 100
C) Find the value of n that gives the first
triangular number over 1000. What is it?
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Pg 75 Q3
Inequality Problems (1)
n(n1) 2
The nth triangular number is given by
A) Find the value of n that gives the first
triangular number over 100
a 1 b 1 c -200
n(n1)gt200 n2 n gt 200 n2 n - 200 gt 0
If n2 n - 200 0
n 13.65 or -14.65
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Pg 75 Q3
Inequality Problems (1)
n(n1) 2
The nth triangular number is given by
A) Find the value of n that gives the first
triangular number over 100
n gt 13.65 or nlt -14.65
n 13.65 gives 100
n(n1)gt200 n2 n gt 200 n2 n - 200 gt 0
n 14 will give the integer solution over 100
B) What is the first triangular number over 100
14 x 15/2 105
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Pg 75 Q3
Inequality Problems (1)
n(n1) 2
The nth triangular number is given by
C) Find the value of n that gives the first
triangular number over 1000. What is it?
a 1 b 1 c -2000
n(n1)gt2000 n2 n gt 2000 n2 n - 2000 gt 0
If n2 n - 2000 0
n 44.22 or -45.22
If n45, number is 1035
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Inequality Problems (2)
A) Solve 2x2 8x 7 0
AQA 2002
Leaving answers as surds
B) Hence solve 2x2 8x 7 gt 0
Solve 2x2 8x 7 0
a 2 b 8 c 7
x -8 ? ?64 - 56 -8 ? ?8 4 4
-8 ? 2?2 4
x -2 1/2 ?2
Or x -2 - 1/2 ?2
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Inequality Problems (2)
A) Solve 2x2 8x 7 0
AQA 2002
Leaving answers as surds
B) Hence solve 2x2 8x 7 gt 0
x -2 1/2 ?2
Or x -2 - 1/2 ?2
Or x lt -2 - 1/2 ?2
x gt -2 1/2 ?2