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Answer =x^2-24x+128

Full solution:

f(x)=x^2 -(alpha + beta)x+ alpha × beta.

Alpha+Beta=24 ..let it be equation 1

Alpha-Beta=8 ..let it be equation 2

Adding equation 1 and 2.

Alpha+Beta=24

Alpha-Beta=8

2Alpha=32

Dividing whole equation by 2.

then,

Alpha = 16 ..equation 3

Subtracting equation 2 from 1.

Alpha+Beta=24

Alpha-Beta=8

- + -

2Beta =16

Dividing whole equation by 2

Beta = 8 ..equation 4

then multiplying equation 3 and 4.

Alpha × Beta = 16×8

Alpha ×Beta = 128

Putting the value in the polynomial formula.

x^2 -(alpha + beta)x+ alpha × beta.

x^2 -(24)x+ 128

=x^2-24x+128