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CBSE Class 10 Answered

if alpha beta are the zeroes of 25psquare -15p+2 then find a quadratic polunomial whose zeroes 1/2alpha and 1/2 beta
Asked by ajayrath7 | 07 Mar, 2019, 12:33: PM
answered-by-expert Expert Answer
f(p) = 25p2 -15p + 2 = 0
 
f(p) = 25p2 -10p -5p +2 = 0
 
f(p) = 5p ( 5p -2 ) -( 5p - 2)  = (5p-2)(5p-1) = 0
 
hence roots are α = 2/5  and β = 1/5
 
if roots are α/2 and β/2 , then the polynomial   g(p)  = p2 - [ (α+β) / 2 ] p +( αβ/4) = 0
 
g(p) = p2 - (3/10)p + (1/50) = 0
 
g(p) = 50 p2 - 15 p + 1 = 0
Answered by Thiyagarajan K | 07 Mar, 2019, 03:15: PM

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