Question
Find the polynomial having roots at $ 1 $ , $ 4 $ , $ 5 $ , $ 7 $ , $ 8 $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-29x^5+335x^4-1955x^3+5984x^2-8816x+4480 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 4 $ | $ x-4 $ |
| $ 5 $ | $ x-5 $ |
| $ 7 $ | $ x-7 $ |
| $ 8 $ | $ x-8 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-4 \right) \cdot \left( x-5 \right) \cdot \left( x-7 \right) \cdot \left( x-8 \right) \cdot \left( x-4 \right) = x^6-29x^5+335x^4-1955x^3+5984x^2-8816x+4480 $$This page was created using
Polynomial From Roots Calculator