Question
Find the polynomial having roots at $ 12 $ , $ 54 $ and $ -21 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^3-45x^2-738x+13608 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 12 $ | $ x-12 $ |
| $ 54 $ | $ x-54 $ |
| $ -21 $ | $ x+21 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-12 \right) \cdot \left( x-54 \right) \cdot \left( x+21 \right) = x^3-45x^2-738x+13608 $$This page was created using
Polynomial From Roots Calculator