Question

find a cubic polynomial , whose zeros are - 2,- 3 and- 1

Answer 1

LET a , b and c be the zeroes of polynomial such that ,

a=-2
b=-3
c=-1

We know any cubic polynomial is of the form :-

p(x)=k[x^3-(a+b+c)x^2+(ab+bc+ca)x-abc]
where k is any non zero constant

Now,

a+b+c=(-1-2-3)=-6

ab+bc+ca=(-1)(-2)+(-2)(-3)+(-3)(-1) =2+6+3=11

abc = (-1)(-2)(-3)=-6

So, the required polynomial is :-

p(x)=k[x^3-(-6)x^2+11x-(-6)] where k is any non zero constant

p(x)=k[x^3+6x^2+11x+6] where k is any non zero constant.....is your answer


Answer :- The required polynomial is

p(x=k[x^3+6x^2+11x+6] where k is any non zero constant...

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