Question
Find the polynomial having roots at $ 1 $ , $ 3 $ , $ 5 $ , $ 7 $ and $ 90993 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-91009x^4+1455974x^3-7825574x^2+16014873x-9554265 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 3 $ | $ x-3 $ |
| $ 5 $ | $ x-5 $ |
| $ 7 $ | $ x-7 $ |
| $ 90993 $ | $ x-90993 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-3 \right) \cdot \left( x-5 \right) \cdot \left( x-7 \right) \cdot \left( x-90993 \right) = x^5-91009x^4+1455974x^3-7825574x^2+16014873x-9554265 $$This page was created using
Polynomial From Roots Calculator