# If #alpha#, #beta# and #gamma# are the roots of the equation #x^3+6x+1=0#, how do you find the polynomial whose roots are #alpha beta# , #beta gamma# and #alpha gamma#?

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#### Explanation

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We know that,

Then, by **Vieta's Rule,** we have,

Let,

Then,

Now,

From

**Enjoy Maths.!**

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#### Answer:

The equation is

#### Explanation:

Let's rewrite the equation as

If

Comparing this equation to the original equation,

The new roots are,

Therefore,

The coefficient of

The coefficient of

The coefficient of

The equation is

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