Question
Find the polynomial having roots at $ 3 $ , $ 6 $ , $ 9 $ , $ 12 $ , $ 15 $ and $ 18 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-63x^5+1575x^4-19845x^3+131544x^2-428652x+524880 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 6 $ | $ x-6 $ |
| $ 9 $ | $ x-9 $ |
| $ 12 $ | $ x-12 $ |
| $ 15 $ | $ x-15 $ |
| $ 18 $ | $ x-18 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x-6 \right) \cdot \left( x-9 \right) \cdot \left( x-12 \right) \cdot \left( x-15 \right) \cdot \left( x-18 \right) = x^6-63x^5+1575x^4-19845x^3+131544x^2-428652x+524880 $$This page was created using
Polynomial From Roots Calculator