Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 1 }{ 3 } $ and $ \dfrac{ 1 }{ 6 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 36x^3-36x^2+11x-1 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ \dfrac{ 1 }{ 6 } $ | $ 6x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( 3x-1 \right) \cdot \left( 6x-1 \right) = 36x^3-36x^2+11x-1 $$This page was created using
Polynomial From Roots Calculator