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Algebra

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29 Dec 2007 20:04:23 IST

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Quadritic Equation

None

Prove that roots of the equation
abc²x² + 3a² cx + b² cx - 6a²-ab +2b²= 0 , are rational.

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abhishek sinha

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Joined: 18 Dec 2007

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29 Dec 2007 22:32:44 IST

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assume root of the form p + sqrt ( q )

put it for x

Now equate the rational & irrational part .

Or ,

Show the discriminant to be a perfect square ( a, b , c are rational )

Abhishek Ambastha

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30 Dec 2007 09:52:09 IST

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Hey! I know that to.
Would u please solve the question, i am unable to factorize the Discriminant

Nadeem

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30 Dec 2007 11:12:19 IST

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The coefficent of a² should be 6 not -6. Otherwise the question is wrong

Bhaskar Tetarbe

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31 Dec 2007 09:31:11 IST

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d Basic is to prove that the discriminant is a perfect sq. To do this find out the
D.
D = (3a²c + b²c)² - 4(abc²)(-6a² - ab + 2b²)
    = c²(9a⁴ + b⁴ + 10a²b² + 24a³b - 8ab³ )
    = c²(9a⁴ + b⁴ + 16a²b² + 24a³b - 8ab³- 6a²b²)
    = c²(3a² - b² + 4ab)²Thus we have found that D is a perfect square therefore the roots will come out to be rational.

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