Question
Find the polynomial having roots at $ 1 $ , $ 2 $ , $ 3 $ , $ 4 $ , $ 5 $ , $ 6 $ , $ 7 $ , $ 8 $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^9-45x^8+870x^7-9450x^6+63273x^5-269325x^4+723680x^3-1172700x^2+1026576x-362880 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 4 $ | $ x-4 $ |
| $ 5 $ | $ x-5 $ |
| $ 6 $ | $ x-6 $ |
| $ 7 $ | $ x-7 $ |
| $ 8 $ | $ x-8 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-4 \right) \cdot \left( x-5 \right) \cdot \left( x-6 \right) \cdot \left( x-7 \right) \cdot \left( x-8 \right) \cdot \left( x-9 \right) = x^9-45x^8+870x^7-9450x^6+63273x^5-269325x^4+723680x^3-1172700x^2+1026576x-362880 $$This page was created using
Polynomial From Roots Calculator