Question
Find the polynomial having roots at $ 9 $ , $ -4 $ , $ 4 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-9x^3-16x^2+144x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 9 $ | $ x-9 $ |
| $ -4 $ | $ x+4 $ |
| $ 4 $ | $ x-4 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-9 \right) \cdot \left( x+4 \right) \cdot \left( x-4 \right) \cdot x = x^4-9x^3-16x^2+144x $$This page was created using
Polynomial From Roots Calculator