Question
Find the polynomial having roots at $ -\dfrac{ 4 }{ 5 } $ , $ \dfrac{ 5 }{ 4 } $ and $ -\dfrac{ 1 }{ 4 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 80x^3-16x^2-89x-20 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 4 }{ 5 } $ | $ 5x+4 $ |
| $ \dfrac{ 5 }{ 4 } $ | $ 4x-5 $ |
| $ -\dfrac{ 1 }{ 4 } $ | $ 4x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+4 \right) \cdot \left( 4x-5 \right) \cdot \left( 4x+1 \right) = 80x^3-16x^2-89x-20 $$This page was created using
Polynomial From Roots Calculator