Question
Find the polynomial having roots at $ -9 $ , $ 1 $ , $ 0 $ , $ 1 $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-2x^4-80x^3+162x^2-81x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -9 $ | $ x+9 $ |
| $ 1 $ | $ x-1 $ |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+9 \right) \cdot \left( x-1 \right) \cdot x \cdot \left( x-1 \right) \cdot \left( x-9 \right) = x^5-2x^4-80x^3+162x^2-81x $$This page was created using
Polynomial From Roots Calculator