Quadratic Equations

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Quadratic Equations

• Learning Outcomes
• Factorise by use of difference of two squares
• Factorise quadratic expressions
• Solve quadratic equations by formula
• Solve 1 linear and 1 quadratic equation
  simultaneously

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Quadratic Equations
Factorisation

• Factorise
• x2 3x
• 2x2 4x
• 3pr pr2
• 6pr3 2pr2
• 4x2y 2xy2 6y2

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Quadratic Equations
Factorisation
Difference of 2 squares
b) (x 2)(x - 2)
a) (x 1)(x - 1)
From the above examples we can conclude
Factorise
(x 3)(x - 3) x2 - 9
Expand
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Quadratic Equations
Factorisation
In general, where a any number
Factorise
(x a)(x a) x2 a2
Expand
a) x2 49
f) b2 c2
b) x2 100
g) 2x2 98
c) x2 121

1. 4x2 49

d) x2 169
i) 4x2 25
e) x2 y2
e) a2x2 y2
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Factorising Quadratic Expressions
Quadratic Equations
Expressions with x2 term often take the following
form ax2 bx c where a, b, c are all numbers
Expand (x 3)(x 5)
(x 2)(x 5)
(x 1)(x 3)
(x 3)(x 4)
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Factorising Quadratic Expressions
Quadratic Equations
Example
Factorise
x2 8x 15
ax2 bx c
a 1 b 8 c 15
Product ac 15 Sum b 8
Look for two numbers which multiply to give
15 and add to equal 8
1 3 15 5
x2 3x 5x 15
x(x 3) 5(x 3)
(x 3) (x 5)
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Factorising Quadratic Expressions
Quadratic Equations
x2 2x 3
2.
x2 5x 6
1.
x2 - 7x 12
2x2 - 3x 2
3.
4.
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Solving Quadratic Equations
Quadratic Equations
x2 9 0
2.
x2 8x 0
1.
2x2 x
4.
4x2 36
3.
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Quadratic Equations
Quadratic Equations
Quadratic (x2 terms) usually take the form ax2
bx c 0
A quadratic expression with 2 terms ax2 bx
or ax2 c
Common Factor ie x2 2x x(x 2)
Difference of two squares ie 4x2 9 (2x
3)(2x 3)
A quadratic expression with 3 terms ax2 bx
c
Product / Sum ie x2 5x 6 p6 s5 (x
3)(x2)
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Quadratic Equations
Quadratic Equations
a)
b)
x2 3x 2 0
2x2 6x 1 0
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Quadratic Equations
Quadratic Equations
Solving quadratic equations not in the form
ax2 bx c 0
1. x2 5x 6
3. (x 2)2 45 x2 (x 1)2
2. x(x 3)x 2
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Quadratic Equations
Solving Simultaneous Equations
Consider y x2 and y 2 x
Curve and line meet at 2 points A and B
y x2
y 2 x
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Quadratic Equations
Additional Notes
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Quadratic Equations
Learning Outcomes At the end of the topic I will
be able to
Can Revise Do Further
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?
Factorise by use of difference of two
squares Factorise quadratic expressions Solv
e quadratic equations by formula Solve 1
linear and 1 quadratic equation simultaneously
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