Question
Find the polynomial having roots at $ 4 $ , $ 5 $ , $ 9 $ , $ 16 $ , $ 26 $ and $ 39 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-99x^5+3613x^4-61557x^3+514066x^2-2008344x+2920320 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ 5 $ | $ x-5 $ |
| $ 9 $ | $ x-9 $ |
| $ 16 $ | $ x-16 $ |
| $ 26 $ | $ x-26 $ |
| $ 39 $ | $ x-39 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( x-5 \right) \cdot \left( x-9 \right) \cdot \left( x-16 \right) \cdot \left( x-26 \right) \cdot \left( x-39 \right) = x^6-99x^5+3613x^4-61557x^3+514066x^2-2008344x+2920320 $$This page was created using
Polynomial From Roots Calculator