As the polynomial 25x^2-10x+4 is quadratic, one can check discriminant to find if rational zeros and / or factors are possible or not. Discriminant of quadratic polynomial (ax^2+bx+c) is (b^2-4ac). If it is negative, no real zeros / factors exist and if it is square of a number, rational zeros / factors are possible.
Here, (b^2-4ac)=((-10)^2-4xx25xx4)=(100-400)=-300 and as such no further real zeros / roots exist, but we can find complex binomials as factors.
As if alpha and beta are zeros of ax^2+bx+c, then ax^2+bx+c=a(x-alpha)(x-beta) and hence let us find zeros of the trinomial using quadratic formula, which gives zeros as (-b+-sqrt(b^2-4ac))/(2a). Hence, zeros of 25x^2-10x+4 are
(-(-10)+-sqrt((-10)^2-4*25*4))/(2*25)=(10+-sqrt(-300))/50
i.e. (10+-10isqrt3)/50=(1+-isqrt3)/5
Hence 25x^2-10x+4=25(x-(1-isqrt3)/5)(x-(1+isqrt3)/5)
= (5x-1+isqrt3)(5x-1-isqrt3)
