Question
Find the polynomial having roots at $ -37 $ , $ -9 $ , $ -4 $ , $ 5 $ , $ 6 $ , $ 17 $ , $ 44 $ and $ 58 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-80x^7-358x^6+121272x^5-1364231x^4-12168520x^3+122783468x^2+134045088x-1733624640 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -37 $ | $ x+37 $ |
| $ -9 $ | $ x+9 $ |
| $ -4 $ | $ x+4 $ |
| $ 5 $ | $ x-5 $ |
| $ 6 $ | $ x-6 $ |
| $ 17 $ | $ x-17 $ |
| $ 44 $ | $ x-44 $ |
| $ 58 $ | $ x-58 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+37 \right) \cdot \left( x+9 \right) \cdot \left( x+4 \right) \cdot \left( x-5 \right) \cdot \left( x-6 \right) \cdot \left( x-17 \right) \cdot \left( x-44 \right) \cdot \left( x-58 \right) = x^8-80x^7-358x^6+121272x^5-1364231x^4-12168520x^3+122783468x^2+134045088x-1733624640 $$This page was created using
Polynomial From Roots Calculator