How can you tell when the roots are equal/unequal, irrational/rational and how many there are from the discriminant?

1 Answer
Apr 15, 2018

See explanation

Explanation:

Discriminant: #b^2-4ac#

Standard form of a quadratic equation: #y=ax^2+bx+c#

If the discriminant is negative, there are 2 imaginary solutions (involving the square root of -1, represented by #i#).

If the discriminant is zero, the equation is a perfect square (ex. #(x-6)^2#). There is only one solution (and one root). In the equation #(x-6)^2#, or #x^2-12x+36#, the solution is #x=6#.

If the discriminant is positive and is a perfect square (ex. #36, 121, 100, 625#), the roots are rational. If the discriminant is positive and is not a perfect square (ex. #84, 52, 700#), the roots are irrational.

A positive discriminant has two real roots (these real roots can be irrational or rational).