CBSE Class 10 Answered
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
Expert Answer
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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