How to use the discriminant to find out what type of solutions the equation has for x^2 = 0?

1 Answer
George C.
May 23, 2015

x^2=0 is of the form ax^2+bx+c = 0, with a=1, b=0 and c=0.

The discriminant is given by the formula:

Delta = b^2-4ac = 0^2 - (4xx1xx0) = 0-0 = 0

This means that x^2=0 has one repeated real root and because 0=0^2 is a perfect square, that repeated root is rational.

The possible cases are:

Delta < 0 No real roots. Two distinct complex roots.
Delta = 0 One repeated, rational, real root.
Delta > 0 Two distinct real roots. If Delta is also a perfect square then those roots are rational.

Severe overkill that it is, you can apply the standard quadratic solution formula to find the (repeated) solution as follows:

x = (-b+-sqrt(Delta))/(2a) = (-0+-sqrt(0))/(2xx1) = 0/2 = 0

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