美夢成真教甄討論區

p是實數，x^3+px^2+22x+40=0 三根成等差，求p

令三根為 a - d，a，a + d
則
-3a = p
3a^2 - d^2 = 22
a(a^2 - d^2) = -40

d^2 = 3a^2 - 22
a(a^2 - 3a^2 + 22) = -40
a^3 - 11a - 20 = 0
a = 4
p = -12