Given : Sum of zeroes = (∝ + β) = 5/2
Product of the zeroes = = 1
Required quadratic polynomial is
x2 – (∝+β)x + ∝β
= x2 – (5/2)x + 1
= 1/2(2x2 – 5x + 2)
Now, find the zeroes of the above polynomial.
Let f(x) = 1/2(2x2 – 5x + 2)
= 1/2(2x2 – 4x – x + 2)
= 1/2(2x(x – 2) – (x – 2))
= 1/2( (2x – 1)(x – 2) )
Substitute f(x) = 0.
1/2( (2x – 1)(x – 2) ) = 0
either (2x – 1) = 0 or (x – 2) = o
x = 1/2 or x = 2
1/2 and 2 are the zeroes of the polynomial.