Question

If x^3+2x^2-3x-1=0 then s-4 is ....​

Answer 1

Answer:

Given : a,b,c are the roots of x

3

+2x

2

−3x−1=0 ....... (i)

Writing

y

1

for x in (i), the transformed equation is

y

3

+3y

2

−2y−1=0

and the given expression is equal to the value of S

3

in this equation.

Here S

1

=a+b+c=−3; ab+bc+ac=−2

S

2

=(a+b+c)

2

−2(ab+bc+ac)=(−3)

2

−2(−2)=13;

and S

3

+3S

2

−2S

1

−3=0;

whence we obtain S

3

=−42.

answer