Question
Find the polynomial having roots at $ 6 $ , $ 8 $ , $ 10 $ and $ 12 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-36x^3+476x^2-2736x+5760 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 6 $ | $ x-6 $ |
| $ 8 $ | $ x-8 $ |
| $ 10 $ | $ x-10 $ |
| $ 12 $ | $ x-12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-6 \right) \cdot \left( x-8 \right) \cdot \left( x-10 \right) \cdot \left( x-12 \right) = x^4-36x^3+476x^2-2736x+5760 $$This page was created using
Polynomial From Roots Calculator