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If -2 is a root of ((z^3) - (8(z^2)) + (9z) + 58 = 0, what are the other two roots?
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In fact, -2 is a root of the given polynomial, and you can check it in one line,
substituting the value of -2 into the polynomial
- + + 58 = -8 - 32 - 18 + 58 = 0.
Therefore, the given polynomial is divisible by (z-2) without a remainer (according to the Remainder theorem)
and you can divide it using standard long division procedure
= z^2 - 10z + 29.
Solve this quadratic equation using the Quadratic Formula
= = = = 5 +- 2i.
ANSWER. Two other roots of the given equation are (5+2i) and (5-2i).
