If the roots of the equation `a x^2-b x+c=0a r ealpha,beta,` then the roots of the equation `b^2c x^2-a b^(2x)+a^3=0` are `1/(alpha^3+alphabeta),1/(beta^3+alphabeta)` b. `1/(alpha^2+alphabeta),1/(beta^2+alphabeta)` c. `1/(alpha^4+alphabeta),1/(beta^4+alphabeta)` d. none of these

Options

A. `(1)/(alpha^(3) + alphabeta), (1)/(beta^(3) + alphabeta)`
B. `(1)/(alpha^(2) + alphabeta), (1)/(beta^(2) + alphabeta)`
C. `(1)/(alpha^(4) + alphabeta), (1)/(beta^(4) + alphabeta)`
D. none of these

Answer

2

Explanation

Multiplying the given equation by `c/a^(3)`, we get
`(b^(2)c^(2))/(a^(3)) x^(2) - (b^(2)c)/(a^(2))x + c = 0`
or `a((bc)/(a^(2))x)^(2) - b((bc)/(a^(2)))x + c = 0`
`rArr (bc)/(a^(2))x = alpha, beta`
`rArr (alpha + beta)alphabeta x = alpha, beta`
`rArr x = (1)/((alpha + beta)alpha),(1)/((alpha + beta)beta)`