Find the value of $p$ for which the $x$-axis is a tangent to C

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I am able not able to do second part of question 10

What i tried

I took out the derivate and equate it to 0

$$0=px^2+2px+3$$

Another equation i found, x-axis intesection

$$0=px^2+4x+1$$

How do i solve them further ??

Thanks in advance