Question

If α and β are the zeroes of the polynomial 25p^2-15p+2 find the quadratic polynomial whose zeroes are 1/2α and 1/2β

Answer 1

Given quadratic eqn. :  25p2 -15p +2 = 0

LHS of above eqn. is factorised and the eqn. is rewritten as (5p-2)(5p-1) = 0

 

hence roots are :   α = 1/5   and   β = 2/5 .

 

hence 1/(2α) = 5/2  and 1/(2β) = 5/4.

 

hene the equation with roots 1/(2α) and 1/(2β) is,  p2 - [ ( 1/(2α) ) + ( 1/(2β) ]p + ( 1/(2α) ) ( 1/(2β) ) = 0  .......................(1)

 

substituting for 1/(2α) and 1/(2β) in above eqn. we get p2 - [ (5/2) + (5/4) ]p + (5/2)(5/4)  =  0  or  8p2 -30p +25 = 0

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