Question
Find the polynomial having roots at $ 1 $ , $ 2 $ , $ 3 $ , $ 9 $ , $ 10 $ , $ 11 $ and $ 16 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-52x^6+1066x^5-10960x^4+59329x^3-163228x^2+208884x-95040 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 9 $ | $ x-9 $ |
| $ 10 $ | $ x-10 $ |
| $ 11 $ | $ x-11 $ |
| $ 16 $ | $ x-16 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-9 \right) \cdot \left( x-10 \right) \cdot \left( x-11 \right) \cdot \left( x-16 \right) = x^7-52x^6+1066x^5-10960x^4+59329x^3-163228x^2+208884x-95040 $$This page was created using
Polynomial From Roots Calculator