Calculate QAP step by step for the given equation. Fill in the values in this markdown to complete the assignment
$$
x^2-x-42 == 0
$$
[Add the gates here]
symbols = [~one, x, ?, ?, ?, ?]
$\vec{s}$ = [1, 7, ?, ?, ?]
$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$
Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$
$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$
Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$
$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$
Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$
$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$
$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$
Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$
$$
A = \begin{bmatrix}
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
\end{bmatrix}
$$
$$
B = \begin{bmatrix}
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
\end{bmatrix}
$$
$$
C = \begin{bmatrix}
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
? & ? & ? & ? & ? & ? \\
\end{bmatrix}
$$
$$
A(x) = \begin{bmatrix}
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
\end{bmatrix}
$$
$$
B(x) = \begin{bmatrix}
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
\end{bmatrix}
$$
$$
C(x) = \begin{bmatrix}
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ?
\\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
?x^3 + ?x^2 + ?x + ? \\
\end{bmatrix}
$$
$$A(x).\vec{s} = ?$$
$$B(x).\vec{s} = ?$$
$$C(x).\vec{s} = ?$$
$$A(x).\vec{s} * B(x).\vec{s} - C(x).\vec{s} = ?$$
Since the above polynomial is equal to $H(x).Z(x)$ it should have roots at x = 1, 2, 3, 4. Verify the same by pasting the polynomial here.
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