If the curve with equation $y=x^3+px^2-4 $ is the tangent on long axis , Find the $p$

Question

question:

If the curve with equation $y=x^3+px^2-4 $ is tangent with x -axis.

Find the $p$

I know:

tangent Means -> y=0 , y'(Slope of the line)=0

How can I get a complete and correct answer?

Thanks for your help

Answer 1

Hints: You can obtain two equations in two unknowns by putting $y = 0$, and by finding $y'$, then setting $y' = 0$.

$$y=x^3+px^2-4 = 0 \iff \ldots$$

$$y' = 3x^2 + 2px = 0 \iff x(3x + 2p) = 0\iff \ldots$$