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 If A, b, and c are the roots of the equation 2x^3-6x^2-15x-3=0, then find a^2 + b^2 + c^2.

 Jun 21, 2022
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If a,b,c are the roots of : \(2x^3-6x^2-15x-3=0\)

Then, by Vietas' formulae:

\(a+b+c=3\) 

\(ab+ac+bc=-\frac{15}{2}\)

\(abc=\frac{3}{2}\)

 

We want: \(a^2+b^2+c^2\)

Using the following identity:

\(a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)\)

Then:

\(a^2+b^2+c^2=3^2-2(-\frac{15}{2})=9+15=24\)

 Jun 22, 2022

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