Question
Find the polynomial having roots at $ -6 $ , $ 0 $ , $ 0 $ , $ 84 $ , $ 4 $ , $ 0 $ , $ 7 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8-89x^7+382x^6+3360x^5-14112x^4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -6 $ | $ x+6 $ |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 84 $ | $ x-84 $ |
| $ 4 $ | $ x-4 $ |
| $ 0 $ | $ x $ |
| $ 7 $ | $ x-7 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+6 \right) \cdot x \cdot x \cdot \left( x-84 \right) \cdot \left( x-4 \right) \cdot x \cdot \left( x-7 \right) \cdot x = x^8-89x^7+382x^6+3360x^5-14112x^4 $$This page was created using
Polynomial From Roots Calculator