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# need help

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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.

Oct 30, 2022

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$$2x^3-6x^2-15x-3=0$$

$$\text{Remember: } a^2+b^2+c^2=(a+b+c)^2-2(ab+bc+ac)$$

By Vieta's formulae:

$$a+b+c=-\dfrac{-6}{2}=3$$

$$ab+bc+ac=\dfrac{-15}{2}$$

Therefore, $$a^2+b^2+c^2=(3)^2-2(\dfrac{-15}{2})=9+15=24$$

Oct 30, 2022