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If for all real values of a one root of ...

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

A

`2x`

B

`x^(2)`

C

`2x^(2)`

D

`2sqrt(x)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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