Polynomial root problem

Xibu4

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Feb 26, 2022
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I'm a bit stumped on a homework question and would greatly appreciate some input.
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Does this mean that gamma is equal to 3 ? If it is how would I go about solving it because wouldn't I get
αβγ=21\alpha \beta \gamma = -21α+β+γ=5\alpha +\beta +\gamma = 5αβ+βγ+γα=1\alpha \beta +\beta \gamma + \gamma \alpha = -1
Am I meant to solve this simultaneously ?
 
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Yes the root you are given is gamma. You could solve simultaneously. Just check your last equation - should your second and third terms be the same [fixed now ]?

BUT, you know that gamma is 3 and you are asked to find the sum and product of alpha and beta, NOT alpha and beta themselves. You really only need the first 2 equations.
 
Yes the root you are given is gamma. You could solve simultaneously. Just check your last equation - should your second and third terms be the same?

BUT, you know that gamma is 3 and you are asked to find the sum and product of alpha and beta, NOT alpha and beta themselves. You really only nee the first 2 equations.
Ohhh ok thank you can't believe I didn't see that.
 
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