Question
Find the polynomial having roots at $ 8 $ , $ 9 $ , $ 5 $ , $ 4 $ , $ -3 $ , $ -54 $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7+30x^6-1106x^5+9840x^4-23951x^3-62790x^2+311256x-233280 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 8 $ | $ x-8 $ |
| $ 9 $ | $ x-9 $ |
| $ 5 $ | $ x-5 $ |
| $ 4 $ | $ x-4 $ |
| $ -3 $ | $ x+3 $ |
| $ -54 $ | $ x+54 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-8 \right) \cdot \left( x-9 \right) \cdot \left( x-5 \right) \cdot \left( x-4 \right) \cdot \left( x+3 \right) \cdot \left( x+54 \right) \cdot \left( x-1 \right) = x^7+30x^6-1106x^5+9840x^4-23951x^3-62790x^2+311256x-233280 $$This page was created using
Polynomial From Roots Calculator