Question

if one of the zeros of the polynomial ax cube + b x square + cX + d find the product of 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