# If one of the zeros of ax^3+bx^2+cx+d is 0 .the product of then other two zeroes is? (a)-c/a,(b)c/a, (c) 0 (d)-b/a

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https://socratic.org/questions/if-one-of-the-zeros-of-cubic-polynimial-is-0-the-product-of-then-other-two-zeroe#469288

explain me few steps in the above link in a given solution

how the two zeroes are the zeroes of a quadratic equation

f(x)=ax3+bx2+cx=x(ax2+bx+c)

So the other two zeros are just the zeros of a quadratic in standard form:

please give me a detailed explanation of the steps given in the problem

+1 vote
If X is one of the zero of the equation then

a*0^3+ b*0^2+c*0+d=0

(X=0)

Gives d=0

So our final equation is

ax^3+bx^2+cx=0

Take X common and transpose it

X(ax^2+bx+c)=0

ax^2+bx+c=0

Now sum of the roots will be equal to  -b/a

And product of root will be c/a