Question
Find the polynomial having roots at $ 0 $ , $ 0 $ , $ 2 $ , $ 2 $ , $ 3 $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-10x^5+37x^4-60x^3+36x^2 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 2 $ | $ x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot x \cdot \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-3 \right) = x^6-10x^5+37x^4-60x^3+36x^2 $$This page was created using
Polynomial From Roots Calculator