Question
Find the polynomial having roots at $ \dfrac{ 7071 }{ 5000 } $ , $ -\dfrac{ 7071 }{ 5000 } $ and $ \dfrac{ 1 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 75000000x^3-25000000x^2-149997123x+49999041 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 7071 }{ 5000 } $ | $ 5000x-7071 $ |
| $ -\dfrac{ 7071 }{ 5000 } $ | $ 5000x+7071 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5000x-7071 \right) \cdot \left( 5000x+7071 \right) \cdot \left( 3x-1 \right) = 75000000x^3-25000000x^2-149997123x+49999041 $$This page was created using
Polynomial From Roots Calculator