Question
Find the polynomial having roots at $ -1 $ , $ 1 $ , $ 3 $ , $ 9 $ , $ 1 $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-16x^5+77x^4-128x^3+3x^2+144x-81 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 1 $ | $ x-1 $ |
| $ 3 $ | $ x-3 $ |
| $ 9 $ | $ x-9 $ |
| $ 1 $ | $ x-1 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-1 \right) \cdot \left( x-3 \right) \cdot \left( x-9 \right) \cdot \left( x-1 \right) \cdot \left( x-3 \right) = x^6-16x^5+77x^4-128x^3+3x^2+144x-81 $$This page was created using
Polynomial From Roots Calculator