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).