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

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user8235304 | Student, Grade 11 | (Level 1) Valedictorian

Posted August 16, 2013 at 5:18 PM via web

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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`

1 Answer | Add Yours

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llltkl | College Teacher | (Level 3) Valedictorian

Posted August 16, 2013 at 5:28 PM (Answer #1)

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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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