Sea P(x) = a elevado 3x elevado4 - 8ax + 4 , en el que a es un número racional ?

Tienes lo siguiente :

<img src="https://tex.z-dn.net/?f=P%28x%29%3Da%5E3x%5E4-8ax%2B4%20%5C%5C%20%20%5C%5CP%282%29%3Da%5E3%282%29%5E4-8a%282%29%2B4%3D16a%5E3-16a%2B4%3D4%20%5C%5C%2016a%5E3-16a%2B4%3D4%20%5C%5C%2016a%5E3-16a%3D0%20%5C%5C%2016a%28a%5E2-1%29%3D0%20%5C%5C%20a%5E2-1%3D0%20%5C%5C%20%28a%2B1%29%28a-1%29%3D0%20%5C%5C%20a_1%3D1%5C%5Ca_2%3D-1%5C%5C%20%5C%5C%20%20P%28-1%29%3Da%5E3%28-1%29%5E4-8a%28-1%29%2B4%3Da%5E3%2B8a%2B4%20%5C%5C%20Si%5C%20%5C%20a%3D-1%5Cto%28-1%29%5E3%2B8%28-1%29%2B4%3D-1-8%2B4%3D%5Cboxed%7B-5%20%3DP%28-1%29%7D%5C%5C%20Si%5C%20%5C%20a_2%3D1%5Cto%281%29%5E3%2B8%281%29%2B4%3D1%2B8%2B4%3D%5Cboxed%7B13%3DP%28-1%29%7D" />

Saludos!