Maths help please

Im stuck on this i just dont know what the question asking me to do.

A line L has equation y = mx + 2 and a curve C has equation y = x² + 3. M is an unknown constant.

A) Write, in terms of m, the quadratic equation that is satisfied by the x coordinates of any point of intersection of L and C

B) Hence find the values of m for which L is a tangent to C.

I need help mostly on a) please 🙏

For part A, the 2 equations are just equal to each other,
So
X^2 + 3 = mx + 2
And then simply to
X^2 + mx + 1 = 0