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  • If a + b + c = 0, then a3 + b3 + c3 = 3abc

Example
If the roots of the equation 2x2 + 8x + m3 = 0 are equal, find the value of m.
Solution
If the roots are equal, then b2 – 4ac = 0.
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Example
If ab are the roots of the equation 2x2 – 4x – 3 = 0, find a + b and ab.
Solution
From the equation a = 2, b = –4, c = –3,
we know that Description: 37869.png Description: 37863.png Description: 37857.png 
 

 
Example
Find the roots of the equation x2 – 8x + 12 = 0.
Solution
From the equation, we have a = 1, b = –8, c = 12
The roots can be found by the relation, Description: 37851.png 
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