Question
Find the polynomial having roots at $ 1000 $ , $ 500 $ , $ 100 $ , $ 50 $ , $ 10 $ , $ 5 $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-1666x^6+756465x^5-94287300x^4+3867532500x^3-45399000000x^2+166625000000x-125000000000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1000 $ | $ x-1000 $ |
| $ 500 $ | $ x-500 $ |
| $ 100 $ | $ x-100 $ |
| $ 50 $ | $ x-50 $ |
| $ 10 $ | $ x-10 $ |
| $ 5 $ | $ x-5 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1000 \right) \cdot \left( x-500 \right) \cdot \left( x-100 \right) \cdot \left( x-50 \right) \cdot \left( x-10 \right) \cdot \left( x-5 \right) \cdot \left( x-1 \right) = x^7-1666x^6+756465x^5-94287300x^4+3867532500x^3-45399000000x^2+166625000000x-125000000000 $$This page was created using
Polynomial From Roots Calculator