Question
Find the polynomial having roots at $ -\dfrac{ 2 }{ 5 } $ , $ \dfrac{ 6 }{ 5 } $ and $ \dfrac{ 4 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 125x^3-200x^2+20x+48 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 2 }{ 5 } $ | $ 5x+2 $ |
| $ \dfrac{ 6 }{ 5 } $ | $ 5x-6 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+2 \right) \cdot \left( 5x-6 \right) \cdot \left( 5x-4 \right) = 125x^3-200x^2+20x+48 $$This page was created using
Polynomial From Roots Calculator