Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 3 } $ , $ \dfrac{ 2 }{ 3 } $ , $ -\dfrac{ 1 }{ 3 } $ , $ -\dfrac{ 2 }{ 3 } $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 81x^5-162x^4-45x^3+90x^2+4x-8 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-1 \right) \cdot \left( 3x-2 \right) \cdot \left( 3x+1 \right) \cdot \left( 3x+2 \right) \cdot \left( x-2 \right) = 81x^5-162x^4-45x^3+90x^2+4x-8 $$This page was created using
Polynomial From Roots Calculator