Question

if ax^3 +bx^2+cx+d are 0 then find the third zero

Answer 1

$ax^3 +bx^2+cx+d=0 \\ x^2(ax+b)+x(c)+d=0 \\ x[x(a+b)+c]+d=0$

We can conclude that $x$ and $d$ must be zero. Otherwise, the equation cannot be true. There are chances of other variables having a 0 value as well. But, $x$ and $d$ are required to have a numerical value of 0 to JUSTIFY the equation.  

Answer 2

The question is:   IF  TWO roots of   a x³ + b x² + c x + d   are 0, then find the third zero.

if two roots of  P(x) = a x³ + b x² + c x + d are zero  that means 

P(0) = 0
=>  a 0³ + b 0² + c 0 + d = 0
 => d = 0

P(x) = x ( ax² + b x + c) 

So one root  of   a x² + b x + c  is 0.   This means that 
       a 0² + b 0 + c = 0          =>  c = 0

Hence, P(x)  =  x * x * ( a x + b)

Thus the third root is  :    x where  a x + b = 0 
       =>   x = - b/a               Answer.
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Simpler method:

The sum of the three  roots of  P(x) a x³ + b x² + c x + d   =  - b/a
    (- coefficient of x² / coefficient of x³)

So if two roots are  0, then the third root is  -b/a.