AS Mathematics

1
AS Mathematics

• Algebra Solving quadratic equations using the
  quadratic formula

2
Objectives

• Be able to solve quadratic equations by use of
  the formula
• x -b vb2 4ac
• 2a

3
Example 1
Solve the equation 3x2 4x - 1 0
sum 4 product 3(-1) -3
If the equation does not factorise, we need to
use an alternative method
We use the quadratic formula
4
To solve equations of the form ax2
bx c 0
Use the quadratic formula x -b vb2 - 4ac 2a
Example 1 contd 3x2 4x - 1 0
a 3, b 4, c -1
x -4 v42 - 4(3)(-1) 2(3)
-4 v16 12 6
Lets practice surds before we go any further!
-4 v28 6
5
v28 v(4 x 7) v4 x v7 2 x v7 2v7
Remember
Can we simplify this?
Factorise
x 0.215, or x -1.55 (to 3 sf)
The equation has two roots, can you sketch the
curve?
What part of the equation is responsible for the
two roots?
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Example 2 Solve 2x2 12x 18 0 using the quadratic formula
a 2, b 12, c 18
x -12 v122 - 4(2)(18) 2(2)
-12 v144 - 144 4
-12 0 4
This equation has only one root.
Sketch the curve.
x -3
What part of the equation is responsible for the
single root?
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Example 3 Solve 3x2 - 12x 16 0 using the quadratic formula
a 3, b -12, c 16
x 12 v122 - 4(3)(16) 2(3)
12 v144 - 192 6
12 v(- 48) 6
What does this tell you about the graph?
Sketch it.