Question
Find the polynomial having roots at $ 4 $ , $ -5 $ , $ -1 $ , $ \dfrac{ 2 }{ 5 } $ , $ 2 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^6-2x^5-115x^4+136x^3+164x^2-80x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ -5 $ | $ x+5 $ |
| $ -1 $ | $ x+1 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ 2 $ | $ x-2 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( x+5 \right) \cdot \left( x+1 \right) \cdot \left( 5x-2 \right) \cdot \left( x-2 \right) \cdot x = 5x^6-2x^5-115x^4+136x^3+164x^2-80x $$This page was created using
Polynomial From Roots Calculator