Question
Find the polynomial having roots at $ -2 $ , $ 0 $ , $ 0 $ , $ 18 $ , $ 3 $ , $ 0 $ , $ 6 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-25x^7+126x^6+36x^5-648x^4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 18 $ | $ x-18 $ |
| $ 3 $ | $ x-3 $ |
| $ 0 $ | $ x $ |
| $ 6 $ | $ x-6 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot x \cdot x \cdot \left( x-18 \right) \cdot \left( x-3 \right) \cdot x \cdot \left( x-6 \right) \cdot x = x^8-25x^7+126x^6+36x^5-648x^4 $$This page was created using
Polynomial From Roots Calculator