Find the polynomial having roots at $ -1 $ , $ 2 $ , $ 8 $ and $ -5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-4x^3-39x^2+46x+80 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 2 $ | $ x-2 $ |
| $ 8 $ | $ x-8 $ |
| $ -5 $ | $ x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-2 \right) \cdot \left( x-8 \right) \cdot \left( x+5 \right) = x^4-4x^3-39x^2+46x+80 $$This page was created using
Polynomial From Roots Calculator