A quadratic equation is one in which the highest power is 2. For example, x2 + 5x + 6 = 0.
Method When Equation is Equal to Zero
The right hand side must be 0 in order to use the following method.
Example 1: Solve x2 + 5x + 6 = 0
Step 1: Factorise the quadratic.
Step 2: Put each factor equal to 0.
(Note: if two brackets are multiplied to give 0, then one of them must be 0).
Step 3: Solve these two simple equations.
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x + 3 =
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0 |
or x + 2 =
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0 |
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x =
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–3 |
x =
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–2 |
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Therefore –3 and –2 are the solutions of the equation.
There are two solutions because of the shape of the graph (refer to study note on graphs).
Example 2: Solve x2 + 7x – 18 = 0.
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(x + 9)(x – 2)
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= 0 |
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x + 9
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= 0 |
or
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x – 2 = 0
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x
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= – 9 |
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x = 2
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Example 3: Solve x2 – 8x + 12 = 0.
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(x – 6)(x – 2)
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= 0 |
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x – 2
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= 0 |
or
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x – 6 = 0
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x
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= 2 |
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x = 6
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Method When Equation is Not Equal to Zero
If the equation given is not equal to zero, then follow this procedure.
Example: Solve x 2 + 5x + 3 = 17.
Make the right side equal to zero by subtracting 17 from both sides.
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x2 + 5x – 14 = 0
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(x + 7)(x – 2) = 0
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x = –7
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or
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x = 2
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