A quadratic with parameter

#parameter#quadratic#discriminant

Statement

For which $m$ does the equation
$x^2+2(m-1)x+m+5=0$
have at least one real root?

Hint

The condition is $\Delta\ge0$ .

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Discriminant. $\Delta=4(m-1)^2-4(m+5)=4(m^2-2m+1-m-5)=4(m^2-3m-4)$ .

Condition. $m^2-3m-4\ge0$ , i.e. $(m-4)(m+1)\ge0$ .

Conclusion. $m\in\,]-\infty,-1]\,\cup\,[4,+\infty[$ .