Question

If alpha, beta, gamma are the roots of the equation x^3+ax^2+bx+c=0 then alpha^-1+beta^-1+gamma^-1=
A) a/c
B) c/a
C) - b/c
D) b/a​

Answer 1

Answer:

Step-by-step explanation:

3:50

If `x^(3)+ax^(2)+bx+c=0` has the roots `alpha^(2)+beta

Answer 2

Answer:

(C) -b/c

Step-by-step explanation:

here in this equation-x^3+ax^2+bx+c=0

A=1

B=a

C=b

D=c

let, alpha=ã

beta=b'

gamma=ç

we know

ã+b'+ç=(-B/A) = (-a) ...... 1

ãb'+b'ç+çã=C/A = (b) ...... 2

ã.b'.ç=(-D/A) = (-c) ...... 3

Let's rearrange: 1/ã+1/b'+1/ç

=>LCM is ã.b'.ç

=>(b'ç+ãç+ãb')/ã.b'.ç

=>using 2 on the numerator and 3 on denominator.

(b'ç+ãç+ãb')/ã.b'.ç = b/(-c)

=>(b'ç+ãç+ãb')/ã.b'.ç= (-b)/c