Question
Find the polynomial having roots at $ -45 $ , $ 21 $ , $ -7 $ , $ 5 $ , $ -12 $ and $ 8 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6+30x^5-924x^4-8954x^3+111627x^2+394380x-3175200 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -45 $ | $ x+45 $ |
| $ 21 $ | $ x-21 $ |
| $ -7 $ | $ x+7 $ |
| $ 5 $ | $ x-5 $ |
| $ -12 $ | $ x+12 $ |
| $ 8 $ | $ x-8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+45 \right) \cdot \left( x-21 \right) \cdot \left( x+7 \right) \cdot \left( x-5 \right) \cdot \left( x+12 \right) \cdot \left( x-8 \right) = x^6+30x^5-924x^4-8954x^3+111627x^2+394380x-3175200 $$This page was created using
Polynomial From Roots Calculator