Question
Find the polynomial having roots at $ -\dfrac{ 5 }{ 3 } $ , $ \dfrac{ 2 }{ 5 } $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^3-41x^2-86x+40 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 5 }{ 3 } $ | $ 3x+5 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+5 \right) \cdot \left( 5x-2 \right) \cdot \left( x-4 \right) = 15x^3-41x^2-86x+40 $$This page was created using
Polynomial From Roots Calculator