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 Post subject: find the roots of a f(x). complex, irrational or rational?Posted: Tue, 13 Mar 2012 02:39:28 UTC
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For a given value of w, the product of the zeroes of f(x)=x^2-3wx+2w^2-1 is 7. Are the roots of f(x) complex, rational or irrational?

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 Post subject: Re: find the roots of a f(x). complex, irrational or rationPosted: Tue, 13 Mar 2012 05:20:58 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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johnsmith wrote:
For a given value of w, the product of the zeroes of f(x)=x^2-3wx+2w^2-1 is 7. Are the roots of f(x) complex, rational or irrational?

Solve for w and use the discriminant, what's the problem?

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 Post subject: Re: find the roots of a f(x). complex, irrational or rationPosted: Tue, 13 Mar 2012 11:30:35 UTC
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Hello, johnsmith!

Quote:
For a given value of , the product of the zeroes of is 7.
Are the roots of complex, rational or irrational?

For this function, the product of the zeroes is , the constant term.

. .

Hence: .

Its discriminant is: .

Therefore, its roots are irrational.

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