Question

For what value(s) of t,25x2_20x+t2 will be a perfect square ?

Answer 1

t value is t=+- 2 . I hope it helpful to u

Answer 2

Given quadratic polynomial : p(x) =  25 x² - 20 x + t²
Find t such that it is a perfect square.

p(x) = (5 x)² - 2 * (5 x) * 2 + t²
       = (5 x)² - 2 ( 5 x) * 2 + 2² + t² - 2²
       = (5 x - 2²)² + t² - 2

     If t² = 2, then p(x) is a perfect square.
        t = √2.