Find the polynomial having roots at $ 0 $ , $ 4 $ , $ 10 $ , $ 16 $ and $ 20 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-50x^4+864x^3-5920x^2+12800x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 4 $ | $ x-4 $ |
| $ 10 $ | $ x-10 $ |
| $ 16 $ | $ x-16 $ |
| $ 20 $ | $ x-20 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-4 \right) \cdot \left( x-10 \right) \cdot \left( x-16 \right) \cdot \left( x-20 \right) = x^5-50x^4+864x^3-5920x^2+12800x $$This page was created using
Polynomial From Roots Calculator