In the quadratic equation `ax^2 + bx + c = 0`, if `Delta = b^2-4ac and alpha + beta, alpha^2 + beta^2, alpha^3 + beta^3` are in GP. where `alpha, beta` are the roots of `ax^2 + bx + c =0`, then

Options

A. `Delta ne 0`
B. `b Delta = 0 `
C. `cb ne 0`
D. `c Delta = 0 `

Answer

D

Explanation

`(-b)/(a) , (b^(2) - 2ac)/(a^(2)) , (-b^(3) + 3abc)/(a^(3))` are in G.P.
`(b^(2) - 2ac)^(2) = (-b^(3) + 3abc)(-b)`
`b^(4) + 4a^(2) c^(2) - 4ab^(2) c = b^(4) - 3ab^(2)c`
`ab^(2)c - 4a^(2)c^(2) = 0`
a.c.`(b^(2) - 4ac) = 0 `
`implies c. Delta = 0 `