The polynomial generated from the given zeros is: $ P(x) = 8x^4-214x^3+1805x^2-4758x+1080 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 10 $ | $ x-10 $ |
$ 12 $ | $ x-12 $ |
$ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
$ \dfrac{ 9 }{ 2 } $ | $ 2x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-10 \right) \cdot \left( x-12 \right) \cdot \left( 4x-1 \right) \cdot \left( 2x-9 \right) = 8x^4-214x^3+1805x^2-4758x+1080 $$