Question

Use the discriminant to describe the roots of each equation. Then select the best description.

2m2 + 3 = m



double root

real and rational root

real and irrational root

imaginary root

Answer 1

\[
2m^2 -m + 3=0\\
b^2-4 ac = 1 - 24 =-23<0

\]
Two imaginary roots

Answer 2

rearrange the equation into the form \[ax^2+bx+c = 0\]the discriminant \((\Delta)\) is then given by \(\Delta = b^2-4ac\)
If \(\Delta = 0\) you have a perfect square and a double root
if \(\Delta > 0\) you have two real roots
if \(\Delta < 0\) you have two imaginary roots
If you can't simplify \(\sqrt{b^2-4ac}\) into something without a radical sign, you've got irrational roots.