How to use the discriminant to find out what type of solutions the equation has for qx^2+rx+s=0?

1 Answer
George C.
May 23, 2015

The discriminant of qx^2+rx+s=0 is given by the formula:

Delta = r^2-4qs

If Delta < 0 then the quadratic equation has no real solutions. It has two distinct complex roots (complex conjugates of one another).

If Delta = 0 then the quadratic equation has one repeated root. If q, r and s are rational then the repeated root is rational too.

If Delta > 0 then the quadratic equation has two distinct real roots. If q, r and s are rational and Delta is the square of a rational number, then the roots will be rational too.

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