Question
Find the polynomial having roots at $ -6 $ , $ -5 $ , $ -3 $ , $ 0 $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5+10x^4+7x^3-162x^2-360x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -6 $ | $ x+6 $ |
| $ -5 $ | $ x+5 $ |
| $ -3 $ | $ x+3 $ |
| $ 0 $ | $ x $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+6 \right) \cdot \left( x+5 \right) \cdot \left( x+3 \right) \cdot x \cdot \left( x-4 \right) = x^5+10x^4+7x^3-162x^2-360x $$This page was created using
Polynomial From Roots Calculator