Question
Find the polynomial having roots at $ 3 $ , $ \dfrac{ 1 }{ 3 } $ , $ 5 $ and $ \dfrac{ 1 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^4-128x^3+290x^2-128x+15 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ 5 $ | $ x-5 $ |
| $ \dfrac{ 1 }{ 5 } $ | $ 5x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( 3x-1 \right) \cdot \left( x-5 \right) \cdot \left( 5x-1 \right) = 15x^4-128x^3+290x^2-128x+15 $$This page was created using
Polynomial From Roots Calculator