Question

If `alpha` and `beta`, `alpha` and `gamma`, `alpha` and `delta` are the roots of the equations `ax^(2)+2bx+c=0`, `2bx^(2)+cx+a=0` and `cx^(2)+ax+2b=0` respectively where `a`, `b`, `c` are positive real numbers, then `alpha+alpha^(2)` is equal to
A. `-1`
B. `1`
C. `0`
D. `abc`

Answer 1

Correct Answer - A
`(a)` `alpha` is root of all equations.
`:.a alpha^(2)+2balpha+c=0`
`2balpha^(2)+calpha+a=0`
`calpha^(2)+aalpha+2b=0`
Adding `(a+2b+c)(1+alpha+alpha^(2))=0`
As `a`,`b`,`c in R^(+)`, `alpha+alpha^(2)=-1`