find the roots of a f(x). complex, irrational or rational?

johnsmith · **Joined:** Mon, 12 Mar 2012 18:17:10 UTC **Posts:** 4

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?

Shadow · **Posted:** Tue, 13 Mar 2012 05:20:58 UTC

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?

Soroban · **Posted:** Tue, 13 Mar 2012 11:30:35 UTC

Hello, johnsmith!

Quote:

For a given value of

, 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?

For this function, the product of the zeroes is 2w^2-1

, the constant term.

. . $2w^2-1 \:=\:7 \quad\Rightarrow\quad w^2 \:=\:4 \quad\Rightarrow\quad w \,=\,\pm2$

Hence: . $f(x) \:=\:x^2 \pm6x + 7$

Its discriminant is: . $(\pm 6)^2 - 4(7) \:=\:8$

Therefore, its roots are irrational.

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find the roots of a f(x). complex, irrational or rational?

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