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mhchen:

I'm given 3 quadratics in the form ax^2 +bx + c And I'm given a 4th quadratic, also in the same form. The question asks me what combination of the 3 quadratics add up to the 4th quadratic. I should use a matrix to solve this but I'm not sure how to arrange the matrix

mhchen:

For example |dw:1571497506557:dw|

SemiDefinite:

Compare like terms: \[\left[\begin{matrix}2 & 1 & 3 \\ 1 & -1 & 2 \\ 4 &3 & 5\end{matrix}\right] \left(\begin{matrix} \alpha \\ \beta \\ \gamma\end{matrix}\right) =\left(\begin{matrix}-9 \\ -7 \\ -15\end{matrix}\right) \]

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