Question
Find the polynomial having roots at $ 0 $ , $ 0 $ , $ 1 $ , $ 1 $ , $ 10 $ , $ 1 $ , $ 11 $ and $ 10 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-34x^7+416x^6-2154x^5+4291x^4-3620x^3+1100x^2 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 1 $ | $ x-1 $ |
| $ 10 $ | $ x-10 $ |
| $ 1 $ | $ x-1 $ |
| $ 11 $ | $ x-11 $ |
| $ 10 $ | $ x-10 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot x \cdot \left( x-1 \right) \cdot \left( x-1 \right) \cdot \left( x-10 \right) \cdot \left( x-1 \right) \cdot \left( x-11 \right) \cdot \left( x-10 \right) = x^8-34x^7+416x^6-2154x^5+4291x^4-3620x^3+1100x^2 $$This page was created using
Polynomial From Roots Calculator