Question
Find the polynomial having roots at $ -250 $ , $ -200 $ , $ -100 $ , $ 0 $ and $ 100 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5+450x^4+40000x^3-4500000x^2-500000000x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -250 $ | $ x+250 $ |
| $ -200 $ | $ x+200 $ |
| $ -100 $ | $ x+100 $ |
| $ 0 $ | $ x $ |
| $ 100 $ | $ x-100 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+250 \right) \cdot \left( x+200 \right) \cdot \left( x+100 \right) \cdot x \cdot \left( x-100 \right) = x^5+450x^4+40000x^3-4500000x^2-500000000x $$This page was created using
Polynomial From Roots Calculator