Question
Find the polynomial having roots at $ 82 $ , $ 45 $ , $ 67 $ , $ 23 $ , $ 17 $ , $ 7 $ and $ 57 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-298x^6+35725x^5-2206810x^4+74685475x^3-1358450062x^2+12035628111x-38570105070 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 82 $ | $ x-82 $ |
| $ 45 $ | $ x-45 $ |
| $ 67 $ | $ x-67 $ |
| $ 23 $ | $ x-23 $ |
| $ 17 $ | $ x-17 $ |
| $ 7 $ | $ x-7 $ |
| $ 57 $ | $ x-57 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-82 \right) \cdot \left( x-45 \right) \cdot \left( x-67 \right) \cdot \left( x-23 \right) \cdot \left( x-17 \right) \cdot \left( x-7 \right) \cdot \left( x-57 \right) = x^7-298x^6+35725x^5-2206810x^4+74685475x^3-1358450062x^2+12035628111x-38570105070 $$This page was created using
Polynomial From Roots Calculator