Question
Find the polynomial having roots at $ 0 $ , $ 1 $ , $ 2 $ , $ 3 $ , $ 7 $ and $ 212 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-225x^5+2809x^4-11319x^3+17638x^2-8904x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 7 $ | $ x-7 $ |
| $ 212 $ | $ x-212 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-7 \right) \cdot \left( x-212 \right) = x^6-225x^5+2809x^4-11319x^3+17638x^2-8904x $$This page was created using
Polynomial From Roots Calculator