Question

How to use the discriminant to find out what type of solutions the equation has for `2x^2 + 5x + 5 = 0`?

Answer 1

`2x^2+5x+5` has discriminant `Delta = -15`

Since `Delta < 0` the equation has no real solutions, only a pair of complex ones.

Explanation:

`2x^2+5x+5` is of the form `ax^2+bx+c`

with `a=2`, `b=5` and `c=5`

This has discriminant given by the formula:

`Delta = b^2-4ac = 5^2-(4xx2xx5) = 25 - 40 = -15`

Since `Delta < 0` the equation has no real solutions, only complex ones.

The possible cases are:

`Delta > 0` : The equation has two distinct real solutions. If `Delta` is a perfect square (and the coefficients of the quadratic are rational) then the roots are rational.

`Delta = 0` : The equation has one (repeated) real solution.

`Delta < 0` : The equation has two distinct complex roots (which are complex conjugates of one another).