Question
Find the polynomial having roots at $ 0 $ , $ 25 $ , $ 50 $ , $ 75 $ and $ 100 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-250x^4+21875x^3-781250x^2+9375000x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 25 $ | $ x-25 $ |
| $ 50 $ | $ x-50 $ |
| $ 75 $ | $ x-75 $ |
| $ 100 $ | $ x-100 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-25 \right) \cdot \left( x-50 \right) \cdot \left( x-75 \right) \cdot \left( x-100 \right) = x^5-250x^4+21875x^3-781250x^2+9375000x $$This page was created using
Polynomial From Roots Calculator