Question

Explain why the discriminant affects the type of roots for a quadratic equation

Answer 1

See below

Explanation:

The roots aka solutions to a quadratic equation in standard form:

`ax^2 + bx + c = 0`
are given by

`x = ( -b \pm √(b^2 - 4ac))/( 2a )`

The term under the square root sign,
`b^2 - 4ac` is called the discriminant

The type and number of roots are determined by the sign of the discriminant

When
`b^2 - 4ac = 0` there is one real root.
When
`b^2 - 4ac > 0` there are two real roots.
When
`b^2 - 4ac < 0` there are two complex(imaginary) roots.