A polynomial equation with parameter

#parameter#roots#discriminant

Statement

Find all real $m$ such that the equation
$x^2-2mx+m+2=0$
has two distinct real roots.

Hint

The condition is $\Delta>0$ .

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Discriminant. $\Delta=4m^2-4(m+2)=4(m^2-m-2)$ .

Condition. $\Delta>0\iff m^2-m-2>0\iff(m-2)(m+1)>0$ .

Conclusion. $m\in\,]-\infty,-1[\,\cup\,]2,+\infty[$ .