If #-1# is one of the zeros of #x^3+ax^2+bx+c=0#, then product of other two roots is?

(a) #b+1-a#
(b) #1-a-b#
(c) #a+b+c#
(d) #c-a-b#

1 Answer
Aug 3, 2017

Answer is (a).

Explanation:

As #-1# is one of the zeros of cubic polynomial #x^3+ax^2+bx+c#,

we have #-1+a-b+c=0# or #a+c=1+b# ........(A)

Further if #alpha,beta# and #gamma# are three zeros,

we should have #(x-alpha)(x-beta)(x-gamma)=0#

and as constant term in the product is #-alphabetagamma#,

comparing it with #x^3+ax^2+bx+c#, we have

#-alphabetagamma=c#

Now taking #alpha=-1#, we have #betagamma=c#

and using (A) product of the other two roots is #c=b+1-a#

and hence answer is (a).