Question

if one of the zero of the cubic polynomial ax cube+bx square+cx+d is zero, the product of the other two zeros

Answer 1

let alpha, beta and gamma be the roots
Given that, one of the roots (take alpha) is zero.
Therefore,
ax3 + bx2 + cx + d = 0
a(x3 + b/a x2 + c/a x + d/a) = 0

b/a = alpha + beta + gamma
= beta + gamma. [since alpha is 0 ]
c/a = alpha*beta + beta*gamma + gamma*alpha
= 0 + beta*gamma + 0
= beta *gamma
d/a = alpha *beta*gamma = 0



The product of other zeros is c/a