Question
Find the polynomial having roots at $ 2 $ , $ 23 $ , $ 1 $ , $ 4 $ , $ 1 $ , $ 4 $ , $ 2 $ , $ 17 $ , $ 3 $ and $ 52 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^{10}-109x^9+4154x^8-73730x^7+681393x^6-3602157x^5+11446052x^4-22098020x^3+25177456x^2-15438784x+3903744 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 23 $ | $ x-23 $ |
| $ 1 $ | $ x-1 $ |
| $ 4 $ | $ x-4 $ |
| $ 1 $ | $ x-1 $ |
| $ 4 $ | $ x-4 $ |
| $ 2 $ | $ x-2 $ |
| $ 17 $ | $ x-17 $ |
| $ 3 $ | $ x-3 $ |
| $ 52 $ | $ x-52 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-23 \right) \cdot \left( x-1 \right) \cdot \left( x-4 \right) \cdot \left( x-1 \right) \cdot \left( x-4 \right) \cdot \left( x-2 \right) \cdot \left( x-17 \right) \cdot \left( x-3 \right) \cdot \left( x-52 \right) = x^{10}-109x^9+4154x^8-73730x^7+681393x^6-3602157x^5+11446052x^4-22098020x^3+25177456x^2-15438784x+3903744 $$This page was created using
Polynomial From Roots Calculator