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Maths
Quadratic Equation

A general quadratic equation is of the general form:
 
ax2 + bx + c = 0,
 
where a, b and c are constants and a  0.
 
The values of x which satisfy the above equation are called the roots of the equation. They are found using this equation:
 

 
b2 - 4ac is called the discriminant of the equation (symbol ). When:
 
 > 0, the roots will be real and different
 = 0, the roots will be real and equal
 < 0, the roots will be complex
 
The roots of a quadratic equation are denoted by the Greek letters  and . The following can then be assumed:
 

 
and
 

 
and the quadratic equation can then be re-written as:
 
.
 
The following useful results can used when analysing roots of a quadratic:
 

 

 

 
.

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