Find the polynomial having roots at $ -1 $ , $ 0 $ , $ 9 $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-6x^3-25x^2-18x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 0 $ | $ x $ |
| $ 9 $ | $ x-9 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot x \cdot \left( x-9 \right) \cdot \left( x+2 \right) = x^4-6x^3-25x^2-18x $$This page was created using
Polynomial From Roots Calculator