Question
Find the polynomial having roots at $ 1 $ , $ 2 $ , $ 7 $ , $ 9 $ and $ 16 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-35x^4+417x^3-2029x^2+3662x-2016 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 7 $ | $ x-7 $ |
| $ 9 $ | $ x-9 $ |
| $ 16 $ | $ x-16 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-7 \right) \cdot \left( x-9 \right) \cdot \left( x-16 \right) = x^5-35x^4+417x^3-2029x^2+3662x-2016 $$This page was created using
Polynomial From Roots Calculator