Question
Find the polynomial having roots at $ \dfrac{ 13 }{ 625 } $ , $ \dfrac{ 13 }{ 625 } $ , $ \dfrac{ 13 }{ 625 } $ and $ \dfrac{ 13 }{ 625 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 152587890625x^4-12695312500x^3+396093750x^2-5492500x+28561 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 13 }{ 625 } $ | $ 625x-13 $ |
| $ \dfrac{ 13 }{ 625 } $ | $ 625x-13 $ |
| $ \dfrac{ 13 }{ 625 } $ | $ 625x-13 $ |
| $ \dfrac{ 13 }{ 625 } $ | $ 625x-13 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 625x-13 \right) \cdot \left( 625x-13 \right) \cdot \left( 625x-13 \right) \cdot \left( 625x-13 \right) = 152587890625x^4-12695312500x^3+396093750x^2-5492500x+28561 $$This page was created using
Polynomial From Roots Calculator