Question
Find the polynomial having roots at $ 1 $ , $ \dfrac{ 37 }{ 10 } $ and $ \dfrac{ 67 }{ 250 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2500x^3-12420x^2+12399x-2479 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 37 }{ 10 } $ | $ 10x-37 $ |
| $ \dfrac{ 67 }{ 250 } $ | $ 250x-67 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( 10x-37 \right) \cdot \left( 250x-67 \right) = 2500x^3-12420x^2+12399x-2479 $$This page was created using
Polynomial From Roots Calculator