Find the polynomial having roots at $ -100 $ , $ -20 $ , $ 0 $ , $ 5 $ and $ 36 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5+79x^4-2740x^3-60400x^2+360000x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -100 $ | $ x+100 $ |
| $ -20 $ | $ x+20 $ |
| $ 0 $ | $ x $ |
| $ 5 $ | $ x-5 $ |
| $ 36 $ | $ x-36 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+100 \right) \cdot \left( x+20 \right) \cdot x \cdot \left( x-5 \right) \cdot \left( x-36 \right) = x^5+79x^4-2740x^3-60400x^2+360000x $$This page was created using
Polynomial From Roots Calculator