Find all real numbers $p$ so that
\[x^4 + 2px^3 + x^2 + 2px + 1 = 0\]has at least two distinct negative real roots.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all real numbers $p$ so that
\[x^4 + 2px^3 + x^2 + 2px + 1 = 0\]has at least two distinct negative real roots.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\left( \frac{3}{4}, \infty \right)
Find all real numbers $p$ so that
\[x^4 + 2px^3 + x^2 + 2px + 1 = 0\]has at least two distinct negative real roots.
train