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# help algebra

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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