SOLUTION: Write the simplest third degree polynomial with integer coefficient that has -2 and square root 5 as zeros

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Question 873059: Write the simplest third degree polynomial with integer coefficient that has -2 and square root 5 as zeros
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
Write the simplest third degree polynomial with integer coefficient that has -2 and square root 5 as zeros
A:
If sqrt%285%29 is a root , then the conjugate -sqrt%285%29 is also a root since the coefficients of the polynomial are integers.
sqrt%285%29 and -sqrt%285%29 are roots of the quadratic equation x%5E2+-+5+=+0. Therefore, the third degree polynomial is %28x+%2B+2%29%28x%5E2+-+5%29+=+0 or highlight%28x%5E3++%2B+2x%5E2+-+5x+-+10+=+0%29.
The polynomial function is highlight%28f%28x%29+=+x%5E3++%2B+2x%5E2+-+5x+-+10%29