Question
Find the polynomial having roots at $ 0 $ , $ 10 $ , $ 2 $ , $ 4 $ and $ -4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-12x^4+4x^3+192x^2-320x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 10 $ | $ x-10 $ |
| $ 2 $ | $ x-2 $ |
| $ 4 $ | $ x-4 $ |
| $ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-10 \right) \cdot \left( x-2 \right) \cdot \left( x-4 \right) \cdot \left( x+4 \right) = x^5-12x^4+4x^3+192x^2-320x $$This page was created using
Polynomial From Roots Calculator