If `a , b ,c` real in G.P., then the roots of the equation `a x^2+b x+c=0` are in the ratio a. `1/2(-1+isqrt(3))` b. `1/2(1-isqrt(3))` `c 1/2(-1-isqrt(3))` d. `1/2(1+isqrt(3))`

Options

A. `(1)/(2) (-1 + isqrt(3))`
B. `(1)/(2) (1 - isqrt(3))`
C. `(1)/(2) (-1 - isqrt(3))`
D. `(1)/(2) (1+ isqrt(3))`

Answer

1,3

Explanation

Given , `b^(2)` = ac
or `((b)/(a))^(2) = (c)/(a)`
or `(-(b)/(a))^(2) = (c)/(a)`
or` (alpha + beta)^(2) = alpha beta`
or `((alpha )/(beta))^(2) + ((alpha)/(beta)) + 1 = 0 `
or ` (alpha)/(beta) = (-1 pm sqrt(3i))/(2) ` (where ` i = sqrt(-1)` .