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The general form of quadratic equations is 
. Depending on the coefficients, the equation may have zero, one, or two real solutions for 
:
The part with the square root is called the discriminant:
Calculating the discriminant is sufficient to know how many solutions does the equation have: for positive 
there are two solutions, if 
there is only one, and for 
there are none.
Viète's theorem
If 
and 
are the roots of quadratic equation , then:
Special consideration should be given to quadratic equation when 
. Thus, it takes this form: 
. In this case the roots can be found following the formulae:
For example:
We see that 
and 
.
We know from the above formulae that 
and 
.
It can be seen that the roots are -2 and 5. You need to solve the system of equations if you cannot see the roots at once.
Knowing these properties of roots of quadratic equation can greatly speed up solving the equations like , thus saving precious time on GMAT.
{{#x:box|You can help by providing examples, specific cases and speed techniques for solving quadratics. A related page on Quadratic inequalities is also needed.}}
