EAMCET Engineering 2010 Solved Paper

Equation, x3−bx2+cx−d=0
Let the roots of this cubic equation in GP are (‌

a

r

,a,ar)
Then, Sum of the roots
‌‌

a

r

+a+ar=−(‌

−b

1

)⇒b
‌⇒‌‌a(‌

1

r

+1+r)=b . . . (i)
and ‌

a

r

⋅a+a⋅ar+ar⋅‌

a

r

=‌

c

1

‌⇒‌‌a2(‌

1

r

+r+1)=c . . . (ii)
Product of the roots
‌

a

r

⋅a⋅ar=−(‌

−d

1

)=d
⇒‌‌a3=d . . . (iii)
Eq. (ii) divided by Eq. (i), we get a=c∕b,
put the value of ' a ' in Eq. (iii)
‌(c∕b)3=d
⇒‌‌c3=b3d