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Let the roots of the polynomial \(x^2 + 7x - 2 \) be \(\alpha \text{ and } \beta\) .  Evaluate  \(\alpha^2 + \beta^2.\)

The answer is not 4.cool

 Dec 24, 2023
 #2
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By the quadratic formula, the roots are (-7 + √57)/2 and (-7 - √57)/2.

 

⍺ = (-7 + √57)/2                β = (-7 - √57)/2

 

2 + β2 = [(-7 + √57)/2]2 + [(-7 - √57)/2]2 = 106 - 14√57 + 106 + 14√57 = 106 + 106 = 212

 Dec 25, 2023
 #3
avatar+33586 
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As follows:

 

 

@Padewolofoofy:  You forgot to divide by 2^2

 Dec 25, 2023
edited by Alan  Dec 25, 2023
 #4
avatar+16 
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woops...

Padewolofoofy  Dec 25, 2023
 #5
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THANK YOU! 53 WAS CORRECT!!!

alibaba  Dec 25, 2023

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