Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 3 } $ , $ \dfrac{ 2 }{ 3 } $ , $ 1 $ and $ -\dfrac{ 2 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 27x^4-36x^3-3x^2+16x-4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ 1 $ | $ x-1 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-1 \right) \cdot \left( 3x-2 \right) \cdot \left( x-1 \right) \cdot \left( 3x+2 \right) = 27x^4-36x^3-3x^2+16x-4 $$This page was created using
Polynomial From Roots Calculator