Find the polynomial having roots at $ 2 $ , $ 0 $ , $ 3 $ , $ 0 $ , $ -6 $ , $ 0 $ , $ -5 $ , $ 0 $ , $ 1 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^{10}+5x^9-25x^8-65x^7+264x^6-180x^5 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 0 $ | $ x $ |
| $ 3 $ | $ x-3 $ |
| $ 0 $ | $ x $ |
| $ -6 $ | $ x+6 $ |
| $ 0 $ | $ x $ |
| $ -5 $ | $ x+5 $ |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot x \cdot \left( x-3 \right) \cdot x \cdot \left( x+6 \right) \cdot x \cdot \left( x+5 \right) \cdot x \cdot \left( x-1 \right) \cdot x = x^{10}+5x^9-25x^8-65x^7+264x^6-180x^5 $$This page was created using
Polynomial From Roots Calculator