Question
Find the polynomial having roots at $ 19 $ , $ 20 $ , $ 21 $ , $ 22 $ and $ 23 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-105x^4+4405x^3-92295x^2+965794x-4037880 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 19 $ | $ x-19 $ |
| $ 20 $ | $ x-20 $ |
| $ 21 $ | $ x-21 $ |
| $ 22 $ | $ x-22 $ |
| $ 23 $ | $ x-23 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-19 \right) \cdot \left( x-20 \right) \cdot \left( x-21 \right) \cdot \left( x-22 \right) \cdot \left( x-23 \right) = x^5-105x^4+4405x^3-92295x^2+965794x-4037880 $$This page was created using
Polynomial From Roots Calculator