Recall that the discriminant of a quadratic equation:
[tex]ax^2+bx+c=0[/tex]
is:
[tex]\Delta=b^2-4ac\text{.}[/tex]
Also, if:
[tex]\begin{cases}\Delta>0\text{ the quadratic equation has 2 different real roots,} \\ \Delta=0\text{ the quadratic equation has 1 root of }multiplicity\text{ 2,} \\ \Delta<0\text{ the quadratic equation has 2 different imaginary roots.}\end{cases}[/tex]
Now, notice that the discriminant of the given equation is:
[tex]\Delta=4^2-4\cdot1\cdot(-2)\text{.}[/tex]
Simplifying the above result we get:
[tex]\Delta=16+8=24.[/tex]
Since 24>0, we get that the given equation has 2 different real roots.
Answer: The given equation has 2 different real roots.
