The polynomial generated from the given zeros is: $ P(x) = 8x^4+2x^3-47x^2+7x+30 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 2 $ | $ x-2 $ |
$ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
$ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( 2x+5 \right) \cdot \left( 4x+3 \right) = 8x^4+2x^3-47x^2+7x+30 $$