Find the polynomial having roots at $ 5 $ , $ 1 $ , $ 17 $ , $ 4 $ and $ 6 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-33x^4+361x^3-1707x^2+3418x-2040 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 5 $ | $ x-5 $ |
| $ 1 $ | $ x-1 $ |
| $ 17 $ | $ x-17 $ |
| $ 4 $ | $ x-4 $ |
| $ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( x-1 \right) \cdot \left( x-17 \right) \cdot \left( x-4 \right) \cdot \left( x-6 \right) = x^5-33x^4+361x^3-1707x^2+3418x-2040 $$This page was created using
Polynomial From Roots Calculator