Question
Find the polynomial having roots at $ -33 $ , $ -22 $ , $ -4 $ , $ 8 $ , $ 13 $ and $ 49 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-11x^5-2051x^4-1565x^3+567874x^2-1530584x-14798784 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -33 $ | $ x+33 $ |
| $ -22 $ | $ x+22 $ |
| $ -4 $ | $ x+4 $ |
| $ 8 $ | $ x-8 $ |
| $ 13 $ | $ x-13 $ |
| $ 49 $ | $ x-49 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+33 \right) \cdot \left( x+22 \right) \cdot \left( x+4 \right) \cdot \left( x-8 \right) \cdot \left( x-13 \right) \cdot \left( x-49 \right) = x^6-11x^5-2051x^4-1565x^3+567874x^2-1530584x-14798784 $$This page was created using
Polynomial From Roots Calculator