Question
Find the polynomial having roots at $ 6 $ , $ -8 $ , $ -5 $ , $ 9 $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-5x^4-95x^3+405x^2+1854x-6480 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 6 $ | $ x-6 $ |
| $ -8 $ | $ x+8 $ |
| $ -5 $ | $ x+5 $ |
| $ 9 $ | $ x-9 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-6 \right) \cdot \left( x+8 \right) \cdot \left( x+5 \right) \cdot \left( x-9 \right) \cdot \left( x-3 \right) = x^5-5x^4-95x^3+405x^2+1854x-6480 $$This page was created using
Polynomial From Roots Calculator