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if alpha , beta  are the zeroes of  25 p square - 15 p +2  then find a quadratic polynomial  whose zeroes  1/2alpha   and  1/2beta
Asked by ajayrath7 | 16 Mar, 2019, 08:45: AM
I assume,  ' 1/2alpha ' means    1/(2α).
Please avoid this kind of ambiguity by using proper paranthesis in future while posting this type of questions
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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
Answered by Thiyagarajan K | 16 Mar, 2019, 11:44: AM

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