Question
Find the polynomial having roots at $ -1 $ , $ 0 $ , $ 2 $ , $ 5 $ , $ 8 $ and $ 10 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-24x^5+191x^4-524x^3+60x^2+800x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 0 $ | $ x $ |
| $ 2 $ | $ x-2 $ |
| $ 5 $ | $ x-5 $ |
| $ 8 $ | $ x-8 $ |
| $ 10 $ | $ x-10 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot x \cdot \left( x-2 \right) \cdot \left( x-5 \right) \cdot \left( x-8 \right) \cdot \left( x-10 \right) = x^6-24x^5+191x^4-524x^3+60x^2+800x $$This page was created using
Polynomial From Roots Calculator