Question
Find the polynomial having roots at $ -\dfrac{ 1 }{ 5 } $ , $ \dfrac{ 2 }{ 5 } $ and $ \dfrac{ 5 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 50x^3-135x^2+21x+10 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 5 } $ | $ 5x+1 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+1 \right) \cdot \left( 5x-2 \right) \cdot \left( 2x-5 \right) = 50x^3-135x^2+21x+10 $$This page was created using
Polynomial From Roots Calculator