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sveta [45]
3 years ago
15

Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0

The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+<em>i</em> is a root, so 6-<em>i</em> is also a root.

So the simplest polynomial you can build with these roots is

(<em>x</em> - (-5)) (<em>x</em> - (6 + <em>i </em>)) (<em>x</em> - (6 - <em>i</em> )) = <em>x</em> ^3 - 7<em>x</em> ^2 - 23<em>x</em> + 185

(first choice)

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