Find the polynomial having roots at $ 8 $ , $ 0 $ , $ -4 $ , $ 0 $ , $ -4 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-48x^4-128x^3 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 8 $ | $ x-8 $ |
| $ 0 $ | $ x $ |
| $ -4 $ | $ x+4 $ |
| $ 0 $ | $ x $ |
| $ -4 $ | $ x+4 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-8 \right) \cdot x \cdot \left( x+4 \right) \cdot x \cdot \left( x+4 \right) \cdot x = x^6-48x^4-128x^3 $$This page was created using
Polynomial From Roots Calculator