Find for what values of \(k\) the equation \[x^2+(3k-7)x+(2k+6)=0\] will have real roots in \(x\).

The red curve here is \(y=x^2+(3k-7)x+(2k+6)=0\).

What tells us how many real roots a quadratic equation has?

What is the discriminant of a quadratic equation?

How does its value determine how many roots of a quadratic are real?