Question
Find the polynomial having roots at $ -250 $ , $ -100 $ , $ 0 $ , $ 100 $ and $ 300 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-50x^4-85000x^3+500000x^2+750000000x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -250 $ | $ x+250 $ |
| $ -100 $ | $ x+100 $ |
| $ 0 $ | $ x $ |
| $ 100 $ | $ x-100 $ |
| $ 300 $ | $ x-300 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+250 \right) \cdot \left( x+100 \right) \cdot x \cdot \left( x-100 \right) \cdot \left( x-300 \right) = x^5-50x^4-85000x^3+500000x^2+750000000x $$This page was created using
Polynomial From Roots Calculator