Find the polynomial having roots at $ -2 $ , $ \dfrac{ 9 }{ 20 } $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 20x^3-29x^2-111x+54 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ \dfrac{ 9 }{ 20 } $ | $ 20x-9 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( 20x-9 \right) \cdot \left( x-3 \right) = 20x^3-29x^2-111x+54 $$This page was created using
Polynomial From Roots Calculator