Question

How to use the discriminant to find out what type of solutions the equation has for `x^2 - 8x + 3 = 0`?

Answer 1

For a quadratic of the form
`ax^2 +bx+c=0`
the discriminant is
`Delta = b^2-4ac`
where
`Delta { (<0 rarr "no Real solutions"),(=0 rarr "1 Real solution"),(>0 rarr "2 Real solutions"):}`

Given
`x^2-8x+3 =0`
`Delta = (-8)^2 -4(1)(3) = 52`

Since `Delta > 0`
this equation has 2 Real solutions.

(By the way, since `sqrt(Delta)` is irrational, both solutions are also irrational.)