Question
Find the polynomial having roots at $ 1 $ , $ 2000 $ , $ 2 $ and $ -12 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-1991x^3-18034x^2+68024x-48000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2000 $ | $ x-2000 $ |
| $ 2 $ | $ x-2 $ |
| $ -12 $ | $ x+12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2000 \right) \cdot \left( x-2 \right) \cdot \left( x+12 \right) = x^4-1991x^3-18034x^2+68024x-48000 $$This page was created using
Polynomial From Roots Calculator