Find the polynomial having roots at $ 2 $ , $ 3 $ , $ 7 $ , $ 9 $ , $ 10 $ and $ 23 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-54x^5+1072x^4-10158x^3+48211x^2-107004x+86940 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 7 $ | $ x-7 $ |
| $ 9 $ | $ x-9 $ |
| $ 10 $ | $ x-10 $ |
| $ 23 $ | $ x-23 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-7 \right) \cdot \left( x-9 \right) \cdot \left( x-10 \right) \cdot \left( x-23 \right) = x^6-54x^5+1072x^4-10158x^3+48211x^2-107004x+86940 $$This page was created using
Polynomial From Roots Calculator