Find the polynomial having roots at $ 3 $ , $ 8 $ , $ -4 $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-4x^3-41x^2+36x+288 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 8 $ | $ x-8 $ |
| $ -4 $ | $ x+4 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x-8 \right) \cdot \left( x+4 \right) \cdot \left( x+3 \right) = x^4-4x^3-41x^2+36x+288 $$This page was created using
Polynomial From Roots Calculator