for what value of k, the given expression is a perfect square

Question

k^2x^2+2(k+1)x+4

Answer 1

Given that k^2x^2 + 2(k + 1)x + 4 is a perfect square.

Perfect square = (x + a)^2 = x^2 +  2ax + a^2

Equating the coefficient of x^2 we get,

                           k^2 = 1 => k = +/- 1

Equating theconstants we get,

                            a^2 = 4 => a = 2

Equating x terms we get,

                            2(k + 1) = 2a

                        => 2k+2 = 2(2)

                        => 2k = 4 -2

                        => k = 2/2 = 1

Therefore k = 1 is the answer as we substitute in the equation we will get x^2 + 4x + 2^2 which is (x+2)^2.