Find the polynomial having roots at $ 0 $ , $ 4 $ , $ -5 $ and $ 6 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-5x^3-26x^2+120x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 4 $ | $ x-4 $ |
| $ -5 $ | $ x+5 $ |
| $ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-4 \right) \cdot \left( x+5 \right) \cdot \left( x-6 \right) = x^4-5x^3-26x^2+120x $$This page was created using
Polynomial From Roots Calculator