Question
Find the polynomial having roots at $ 4 $ , $ \dfrac{ 1 }{ 40 } $ , $ \dfrac{ 1 }{ 38 } $ , $ \dfrac{ 3 }{ 112 } $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 170240x^5-1375216x^4+2830554x^3-215507x^2+5560x-48 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ \dfrac{ 1 }{ 40 } $ | $ 40x-1 $ |
| $ \dfrac{ 1 }{ 38 } $ | $ 38x-1 $ |
| $ \dfrac{ 3 }{ 112 } $ | $ 112x-3 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( 40x-1 \right) \cdot \left( 38x-1 \right) \cdot \left( 112x-3 \right) \cdot \left( x-4 \right) = 170240x^5-1375216x^4+2830554x^3-215507x^2+5560x-48 $$This page was created using
Polynomial From Roots Calculator