Question

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

Answer 1

For example

Answer 2

Compare like terms:


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