Find the polynomial having roots at $ -1 $ , $ 2 $ , $ 3 $ and $ -8 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4+4x^3-31x^2+14x+48 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ -8 $ | $ x+8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x+8 \right) = x^4+4x^3-31x^2+14x+48 $$This page was created using
Polynomial From Roots Calculator