If for all real values of a one root of the equation `x^2-3ax + f(a)=0` is double of the other, then f(x) is equal to

Options

A. `2x`
B. `x^(2)`
C. `2x^(2)`
D. `2sqrt(x)`

Answer

C

Explanation

Let `alpha` beone of
`x^(2)-3ax+f(a)=0`
`impliesalpha+2alpha=3alphaimplies3alpha=3a`
`impliesalpha=a` …………i
and `alpha.2alpha=f(a)`
`impliesf(a)=2alpha^(2)=2alpha^(2)` [ using Eq. (i)]
`impliesf(x)=2x^(2)`