Question

for which values of t makes perfect square x^2-tx+1/4

Answer 1

let us equate the given equation with some
equation like (x-k)^2 such that it is a perfect square number, that is
x^2-tx+1/4 = (x-k) ^2 = x^2-2kx+k^2
let us equate the coefficients on both sides
clearly here k^2=1/4=(1/2)^2
therefore k=1/2
and also we have
-t = -2k
t = 2(1/2)=1
hence the value of t is 1