Find the polynomial having roots at $ 1 $ , $ -4 $ , $ 0 $ and $ -1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4+4x^3-x^2-4x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ -4 $ | $ x+4 $ |
| $ 0 $ | $ x $ |
| $ -1 $ | $ x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x+4 \right) \cdot x \cdot \left( x+1 \right) = x^4+4x^3-x^2-4x $$This page was created using
Polynomial From Roots Calculator