Question
Find the polynomial having roots at $ 117 $ , $ 50 $ , $ 7 $ , $ -45 $ , $ 46 $ and $ \dfrac{ 567 }{ 100 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 100x^6-18067x^5+611525x^4+28316359x^3-1625861637x^2+16691561460x-48062605500 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 117 $ | $ x-117 $ |
| $ 50 $ | $ x-50 $ |
| $ 7 $ | $ x-7 $ |
| $ -45 $ | $ x+45 $ |
| $ 46 $ | $ x-46 $ |
| $ \dfrac{ 567 }{ 100 } $ | $ 100x-567 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-117 \right) \cdot \left( x-50 \right) \cdot \left( x-7 \right) \cdot \left( x+45 \right) \cdot \left( x-46 \right) \cdot \left( 100x-567 \right) = 100x^6-18067x^5+611525x^4+28316359x^3-1625861637x^2+16691561460x-48062605500 $$This page was created using
Polynomial From Roots Calculator