The polynomial generated from the given zeros is: $ P(x) = 4x^3-4x^2-11x+6 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ 2 $ | $ x-2 $ |
$ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( x-2 \right) \cdot \left( 2x+3 \right) = 4x^3-4x^2-11x+6 $$