Question

Find the value of the discriminant and describe the number and type of roots.
3x2 - 8x + 2 = 0

Answer 1

If you have a quadratic in the form \(ax^2+bx+c = 0\) the discriminant is given by \[b^2-4ac\]
The value of the discriminant will tell you the nature of the roots of the quadratic.

Discriminant > 0 means 2 real roots
Discriminant = 0 means it is a perfect square, and you have two identical real roots (square root portion in the quadratic formula = 0, so root is just -b/2a, which you may recognize as the x-value of the vertex of the parabola)
Discriminant < 0 means 2 complex roots of the form \(a \pm bi\) where \(i = \sqrt{-1}\)