Question
Find the polynomial having roots at $ 16 $ , $ 31 $ , $ 57 $ , $ 99 $ , $ 163 $ and $ 256 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-622x^5+140256x^4-14457730x^3+708464959x^2-15468638448x+116793667584 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 16 $ | $ x-16 $ |
| $ 31 $ | $ x-31 $ |
| $ 57 $ | $ x-57 $ |
| $ 99 $ | $ x-99 $ |
| $ 163 $ | $ x-163 $ |
| $ 256 $ | $ x-256 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-16 \right) \cdot \left( x-31 \right) \cdot \left( x-57 \right) \cdot \left( x-99 \right) \cdot \left( x-163 \right) \cdot \left( x-256 \right) = x^6-622x^5+140256x^4-14457730x^3+708464959x^2-15468638448x+116793667584 $$This page was created using
Polynomial From Roots Calculator