Question
Find the polynomial having roots at $ 3 $ , $ -5 $ , $ 2 $ , $ -8 $ , $ 7 $ , $ 6 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-5x^6-81x^5+461x^4+1028x^3-8244x^2+10080x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ -5 $ | $ x+5 $ |
| $ 2 $ | $ x-2 $ |
| $ -8 $ | $ x+8 $ |
| $ 7 $ | $ x-7 $ |
| $ 6 $ | $ x-6 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x+5 \right) \cdot \left( x-2 \right) \cdot \left( x+8 \right) \cdot \left( x-7 \right) \cdot \left( x-6 \right) \cdot x = x^7-5x^6-81x^5+461x^4+1028x^3-8244x^2+10080x $$This page was created using
Polynomial From Roots Calculator