$p^2x + py + 8 = 0$
(1;−6)
$p^2 * 1 + p * (-6) + 8 = 0$
$p^2 - 6p + 8 = 0$
$(p^2 - 6p + 9) - 1 = 0$
$(p - 3)^2 - 1^2 = 0$
(p − 3 − 1)(p − 3 + 1) = 0
(p − 4)(p − 2) = 0
p − 4 = 0
p = 4
или
p − 2 = 0
p = 2
Ответ: при p = 2 и p = 4

$p^2x + py + 8 = 0$
(−1;2)
$p^2 * (-1) + p * 2 + 8 = 0$
$-p^2 + 2p + 8 = 0$ | * (−1)
$p^2 - 2p - 8 = 0$
$p^2 - 4p + 2p - 8 = 0$
$(p^2 - 4p) + (2p - 8) = 0$
p(p − 4) + 2(p − 4) = 0
(p − 4)(p + 2) = 0
p − 4 = 0
p = 4
или
p + 2 = 0
p = −2
Ответ: −2; 4.