Question
Find the polynomial having roots at $ 10 $ , $ 7 $ , $ -8 $ , $ 22 $ , $ 6 $ and $ 11 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-48x^5+725x^4-2278x^3-37812x^2+342232x-813120 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 10 $ | $ x-10 $ |
| $ 7 $ | $ x-7 $ |
| $ -8 $ | $ x+8 $ |
| $ 22 $ | $ x-22 $ |
| $ 6 $ | $ x-6 $ |
| $ 11 $ | $ x-11 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-10 \right) \cdot \left( x-7 \right) \cdot \left( x+8 \right) \cdot \left( x-22 \right) \cdot \left( x-6 \right) \cdot \left( x-11 \right) = x^6-48x^5+725x^4-2278x^3-37812x^2+342232x-813120 $$This page was created using
Polynomial From Roots Calculator