$x^2 -(2p+4)x + 3p+4$

Question

$x_1, x_2 =$ the roots

$x_1,p,x_2,...$ = geometric sequence

Find the 12th element of the geometric sequence

What i know is $x_1+x_2=2p+4$

$x_1x_2=3p+4$

I get $-p=x_1+x_2-x_1x_2$

But how to solve for the roots and $p$?

Answer 1

Hint:

We have $$p^2=x_1x_2=3p+4$$

Solve for $p$