Question
Find the polynomial having roots at $ 5 $ , $ \dfrac{ 1 }{ 3 } $ and $ -\dfrac{ 4 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 9x^3-36x^2-49x+20 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 5 $ | $ x-5 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ -\dfrac{ 4 }{ 3 } $ | $ 3x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( 3x-1 \right) \cdot \left( 3x+4 \right) = 9x^3-36x^2-49x+20 $$This page was created using
Polynomial From Roots Calculator