Question

kx^2+4x+k is a perfect square find value of k​

Answer 1

Answer:

k= 2

it satisfies

the statement

Answer 2

Answer:

k=±2

Step-by-step explanation:

For an equation to be a perfect square, it's discriminant should be 0

Let's find out the discriminant of this equation

$b = 4 \\ a = k \\ c = k \\ d = \ {b}^{2} - 4ac \\ d = {4}^{2} - 4 \times k \times k\\ d = 0 \\ 0 = {4}^{2} - 4 {k}^{2} \\ 0 = (4 - 2k)(4 + 2k) \\ k = 2 \: or \: k = - 2 \\ equation \: will \: be \\ 2 {x}^{2} + 4x + 2 \\ 2({x}^{2} + 2x + 1) \\ 2 {(x + 1)}^{2} \\ or \\ - 2 {x}^{2} + 4x - 2 \\ 2( - {x}^{2} + 2x - 1) \\ - 2( {x}^{2} - 2x + 1) \\ - 2 {( x+ 1)}^{2}$