Question
Find the polynomial having roots at $ 2 $ , $ 3 $ , $ 5 $ , $ 7 $ , $ 11 $ , $ 13 $ , $ 17 $ , $ 19 $ and $ 23 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^9-100x^8+4222x^7-98190x^6+1376640x^5-11970750x^4+64002818x^3-201123530x^2+334406399x-223092870 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 5 $ | $ x-5 $ |
| $ 7 $ | $ x-7 $ |
| $ 11 $ | $ x-11 $ |
| $ 13 $ | $ x-13 $ |
| $ 17 $ | $ x-17 $ |
| $ 19 $ | $ x-19 $ |
| $ 23 $ | $ x-23 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-5 \right) \cdot \left( x-7 \right) \cdot \left( x-11 \right) \cdot \left( x-13 \right) \cdot \left( x-17 \right) \cdot \left( x-19 \right) \cdot \left( x-23 \right) = x^9-100x^8+4222x^7-98190x^6+1376640x^5-11970750x^4+64002818x^3-201123530x^2+334406399x-223092870 $$This page was created using
Polynomial From Roots Calculator