Question

if alpha and beta are zeros of polynomial 6 xsquare - 7 x minus 3 form quadratic polynomial whose zeros are 2 alpha and 2 beta

Answer 1

The polynomial can be factored into: (x+1)(2x-5), so we have α = -1 and β = 5/2

 

(i)  The polynomial with zeros α2 and β2 can be factored as (x - α2)(x - β2).   This can be multiplied out to get 

x2 - (α2 + β2)x + α2β2    or    x2 - (1 + 25/4)x + 25/4    or    x2 -  (29/4)x + 25/4  

 

Multiply all the terms by 4 to get   4x2 -  29x + 25

 

See if you can now do part (ii)
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