Question
Find the polynomial having roots at $ \dfrac{ 2 }{ 3 } $ , $ -\dfrac{ 2 }{ 3 } $ and $ \dfrac{ 5 }{ 6 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 54x^3-45x^2-24x+20 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ \dfrac{ 5 }{ 6 } $ | $ 6x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-2 \right) \cdot \left( 3x+2 \right) \cdot \left( 6x-5 \right) = 54x^3-45x^2-24x+20 $$This page was created using
Polynomial From Roots Calculator