Question
Find the polynomial having roots at $ -1 $ , $ 0 $ , $ -7 $ , $ 0 $ , $ 5 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6+3x^5-33x^4-35x^3 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 0 $ | $ x $ |
| $ -7 $ | $ x+7 $ |
| $ 0 $ | $ x $ |
| $ 5 $ | $ x-5 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot x \cdot \left( x+7 \right) \cdot x \cdot \left( x-5 \right) \cdot x = x^6+3x^5-33x^4-35x^3 $$This page was created using
Polynomial From Roots Calculator