Find a polynomial that has the given degree and zeros.
1 answer:
You can write such a cubic polynomial in terms of its roots using the factor theorem:
(<em>x</em> - (-1)) (<em>x</em> - 3) (<em>x</em> - (-5)) = (<em>x</em> + 1) (<em>x</em> - 3) (<em>x</em> + 5)
Now just expand this:
(<em>x</em> + 1) (<em>x</em> - 3) (<em>x</em> + 5) = <em>x</em> ³ + (1 - 3 + 5) <em>x</em> ² + (-3 + 5 - 15) <em>x</em> - 15
… = <em>x</em> ³ + 3<em>x</em> ² - 13<em>x</em> - 15
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