Question
Find the polynomial having roots at $ \dfrac{ 2 }{ 3 } $ , $ -1 $ , $ 1 $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^4-11x^3+3x^2+11x-6 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -1 $ | $ x+1 $ |
| $ 1 $ | $ x-1 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-2 \right) \cdot \left( x+1 \right) \cdot \left( x-1 \right) \cdot \left( x-3 \right) = 3x^4-11x^3+3x^2+11x-6 $$This page was created using
Polynomial From Roots Calculator