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

1 Answer
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.