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Find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1. Hence, find the zeroes if their polynomial.

Answer :

keerthika1998lekha
Let α and β be the zeros of the equation:
Sum of the zeros α+β = -b/a = 5/2...........(!)
Product of zeros αβ = c/a = 1..................(!!)
from (!!) α = 1/β .....................................(!!!)
Substitute (!!!) in (!)
1/β + β = 5/2
(1 + β²)/β = 5/2
2 + 2β² = 5β
2β² - 5β + 2 = 0
2β² - 4β - β + 2 = 0
2β(β - 2) -1(β - 2) = 0 
(2β - 1)(β - 2) = 0
β = 1/2 , 2

Substituting β value in (!!!)
α = 1/1/2 , 1/2 = 2,1/2
a+b=5/2
ab=1
a(5/2-a)=1
5a/2-a^2=1
5a-2a^2=2
2a^2-5a+2=0
2a^2-4a-a+2=0
(2a-1)(a-2)=0
a=1/2,a=2

if a=2,b=1/2
if a=1/2,b=2

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