In the quadratic equation `ax^2+bx+c=0,Delta = b^2-4ac and alpha+beta,alpha^2+beta^2,alpha^3+beta^3,` are in G.P , where `alpha,beta` are the roots of `ax^2+bx+c,` then (a) `Delta != 0` (b) `bDelta = 0` (c) `cDelta = 0` (d) `Delta = 0`

Options

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

Answer

C

Explanation

As `alpha + beta, alpha^(2) + beta^(2) and alpha^(3) + beta^(3)` are in G.P.
`therefore" "(alpha^(2)+beta^(2))^(2)=(alpha+beta)(alpha^(3)+beta^(3))`
`rArr" "alpha beta(alpha^(2)+beta^(2)-2 alpha beta) = 0`
`rArr" "alpha beta(alpha-beta)^(2) = 0`
`rArr" "alpha beta = 0 or alpha = beta rArr (c)/(a) = 0 or Delta = 0 rArr c Delta = 0`