Exercise · ZW-FUNDAMENTAL-THEOREM-OF-ALGEBRA-006 · ★★☆ Intermediate
The product of the three roots of \(z^3+2z^2-z-10\) is:
Choose one option.
Show answer
- A. \(10\)
Explanation
The constant term is \((-1)^3z_1z_2z_3\cdot 1=-10\), so \(z_1z_2z_3=10\).
Review the concept: Fundamental theorem of algebra
Every non-constant polynomial \(p\) with complex coefficients, of degree \(n\), has at least one root in \(\mathbb{C}\); hence it splits into \(n\) linear factors \(z-z_k\), with leading coefficient \(a_n\).
\[p(z)=a_n\prod_{k=1}^{n}(z-z_k)\]
More practice problems: fundamental theorem of algebra
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