Question
Find the polynomial having roots at $ 1 $ , $ 2 $ , $ -7 $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4+6x^3-11x^2-24x+28 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ -7 $ | $ x+7 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x+7 \right) \cdot \left( x+2 \right) = x^4+6x^3-11x^2-24x+28 $$This page was created using
Polynomial From Roots Calculator