Q. If one root of the equation `x^2-3ax+f(a)=0` is double of the other,then `f(x)` =? A) `2x` B) `x^2` C) `2x^2` D) `x`

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llltkl | College Teacher | (Level 3) Valedictorian

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Let one of the roots of the equation `x^2-3ax+f(a)` be p, and the other root is 2p.

Then the equation can be written as: `(x-p)(x-2p)=0`

`rArr x^2--3px+2p^2=0`

Comparing the coefficient of `x` , we get

`-3p=-3a`

`rArr p=a`

Again, comparing the constant term,

`f(a)=2p^2=2a^2`

Therefore, `f(x)=2x^2`

Hence option C) is correct.

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