Question

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

Answer 1

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).