Question
Find the polynomial having roots at $ 1 $ , $ \dfrac{ 4 }{ 23 } $ , $ 56 $ , $ \dfrac{ 14 }{ 25 } $ and $ -55 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 575x^5-1572x^4-1769525x^3+3070226x^2-1472184x+172480 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 4 }{ 23 } $ | $ 23x-4 $ |
| $ 56 $ | $ x-56 $ |
| $ \dfrac{ 14 }{ 25 } $ | $ 25x-14 $ |
| $ -55 $ | $ x+55 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( 23x-4 \right) \cdot \left( x-56 \right) \cdot \left( 25x-14 \right) \cdot \left( x+55 \right) = 575x^5-1572x^4-1769525x^3+3070226x^2-1472184x+172480 $$This page was created using
Polynomial From Roots Calculator