Question
Find the polynomial having roots at $ 10 $ , $ 20 $ , $ 30 $ , $ 40 $ , $ 50 $ and $ 60 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-210x^5+17500x^4-735000x^3+16240000x^2-176400000x+720000000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 10 $ | $ x-10 $ |
| $ 20 $ | $ x-20 $ |
| $ 30 $ | $ x-30 $ |
| $ 40 $ | $ x-40 $ |
| $ 50 $ | $ x-50 $ |
| $ 60 $ | $ x-60 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-10 \right) \cdot \left( x-20 \right) \cdot \left( x-30 \right) \cdot \left( x-40 \right) \cdot \left( x-50 \right) \cdot \left( x-60 \right) = x^6-210x^5+17500x^4-735000x^3+16240000x^2-176400000x+720000000 $$This page was created using
Polynomial From Roots Calculator