Find the polynomial having roots at $ -3 $ , $ 0 $ , $ 3 $ , $ 6 $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-15x^4+45x^3+135x^2-486x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -3 $ | $ x+3 $ |
| $ 0 $ | $ x $ |
| $ 3 $ | $ x-3 $ |
| $ 6 $ | $ x-6 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+3 \right) \cdot x \cdot \left( x-3 \right) \cdot \left( x-6 \right) \cdot \left( x-9 \right) = x^5-15x^4+45x^3+135x^2-486x $$This page was created using
Polynomial From Roots Calculator