Question
Find the polynomial having roots at $ -9 $ , $ 0 $ , $ 9 $ , $ 18 $ , $ 27 $ , $ 36 $ and $ 45 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-126x^6+5670x^5-102060x^4+321489x^3+9093546x^2-63772920x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -9 $ | $ x+9 $ |
| $ 0 $ | $ x $ |
| $ 9 $ | $ x-9 $ |
| $ 18 $ | $ x-18 $ |
| $ 27 $ | $ x-27 $ |
| $ 36 $ | $ x-36 $ |
| $ 45 $ | $ x-45 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+9 \right) \cdot x \cdot \left( x-9 \right) \cdot \left( x-18 \right) \cdot \left( x-27 \right) \cdot \left( x-36 \right) \cdot \left( x-45 \right) = x^7-126x^6+5670x^5-102060x^4+321489x^3+9093546x^2-63772920x $$This page was created using
Polynomial From Roots Calculator