Find the polynomial having roots at $ 2 $ , $ 2 $ , $ 2 $ , $ 2 $ , $ 2 $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-12x^5+60x^4-160x^3+240x^2-192x+64 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( x-2 \right) = x^6-12x^5+60x^4-160x^3+240x^2-192x+64 $$This page was created using
Polynomial From Roots Calculator