Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 4 }{ 5 } $ and $ \dfrac{ 8 }{ 9 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 90x^3-197x^2+140x-32 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
| $ \dfrac{ 8 }{ 9 } $ | $ 9x-8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( 5x-4 \right) \cdot \left( 9x-8 \right) = 90x^3-197x^2+140x-32 $$This page was created using
Polynomial From Roots Calculator