Question
Find the polynomial having roots at $ -1 $ , $ 1 $ , $ 3 $ , $ -4 $ , $ 5 $ and $ -8 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6+4x^5-50x^4-80x^3+529x^2+76x-480 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 1 $ | $ x-1 $ |
| $ 3 $ | $ x-3 $ |
| $ -4 $ | $ x+4 $ |
| $ 5 $ | $ x-5 $ |
| $ -8 $ | $ x+8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-1 \right) \cdot \left( x-3 \right) \cdot \left( x+4 \right) \cdot \left( x-5 \right) \cdot \left( x+8 \right) = x^6+4x^5-50x^4-80x^3+529x^2+76x-480 $$This page was created using
Polynomial From Roots Calculator