Question
Find the polynomial having roots at $ -1 $ , $ \dfrac{ 2 }{ 5 } $ and $ \dfrac{ 4 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 25x^3-5x^2-22x+8 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( 5x-2 \right) \cdot \left( 5x-4 \right) = 25x^3-5x^2-22x+8 $$This page was created using
Polynomial From Roots Calculator