Question
Find the polynomial having roots at $ 132 $ , $ 1 $ , $ 257 $ , $ 2 $ , $ 278 $ , $ 3 $ , $ 281 $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-958x^7+339008x^6-52679578x^5+3155168891x^4-28244547352x^3+95228104852x^2-133688185632x+63601800768 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 132 $ | $ x-132 $ |
| $ 1 $ | $ x-1 $ |
| $ 257 $ | $ x-257 $ |
| $ 2 $ | $ x-2 $ |
| $ 278 $ | $ x-278 $ |
| $ 3 $ | $ x-3 $ |
| $ 281 $ | $ x-281 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-132 \right) \cdot \left( x-1 \right) \cdot \left( x-257 \right) \cdot \left( x-2 \right) \cdot \left( x-278 \right) \cdot \left( x-3 \right) \cdot \left( x-281 \right) \cdot \left( x-4 \right) = x^8-958x^7+339008x^6-52679578x^5+3155168891x^4-28244547352x^3+95228104852x^2-133688185632x+63601800768 $$This page was created using
Polynomial From Roots Calculator