Question
Find the polynomial having roots at $ 8 $ , $ 12 $ , $ 13 $ , $ 16 $ , $ 17 $ and $ 18 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-84x^5+2905x^4-52878x^3+533512x^2-2823744x+6110208 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 8 $ | $ x-8 $ |
| $ 12 $ | $ x-12 $ |
| $ 13 $ | $ x-13 $ |
| $ 16 $ | $ x-16 $ |
| $ 17 $ | $ x-17 $ |
| $ 18 $ | $ x-18 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-8 \right) \cdot \left( x-12 \right) \cdot \left( x-13 \right) \cdot \left( x-16 \right) \cdot \left( x-17 \right) \cdot \left( x-18 \right) = x^6-84x^5+2905x^4-52878x^3+533512x^2-2823744x+6110208 $$This page was created using
Polynomial From Roots Calculator