Find the polynomial having roots at $ 2 $ , $ 0 $ , $ 8 $ , $ 0 $ , $ 1 $ , $ 0 $ , $ 6 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-17x^7+92x^6-172x^5+96x^4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 0 $ | $ x $ |
| $ 8 $ | $ x-8 $ |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 0 $ | $ x $ |
| $ 6 $ | $ x-6 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot x \cdot \left( x-8 \right) \cdot x \cdot \left( x-1 \right) \cdot x \cdot \left( x-6 \right) \cdot x = x^8-17x^7+92x^6-172x^5+96x^4 $$This page was created using
Polynomial From Roots Calculator