Question
Find the polynomial having roots at $ 1 $ , $ 10 $ , $ 100 $ , $ 1000 $ and $ 1001 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-2112x^4+1224221x^3-113333110x^2+1113111000x-1001000000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 10 $ | $ x-10 $ |
| $ 100 $ | $ x-100 $ |
| $ 1000 $ | $ x-1000 $ |
| $ 1001 $ | $ x-1001 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-10 \right) \cdot \left( x-100 \right) \cdot \left( x-1000 \right) \cdot \left( x-1001 \right) = x^5-2112x^4+1224221x^3-113333110x^2+1113111000x-1001000000 $$This page was created using
Polynomial From Roots Calculator