Answer:
For k= +4, the polynomial has two equal roots.
For k = -4, the polynomial has two equal roots.
Step-by-step explanation:
Here, the given expression is :[tex]x^{2} + kx + 4 = 0[/tex]
(1) Now, let us assume the value of k = +4
So, the expression is [tex]x^{2} + 4x + 4 = 0[/tex]
Simplifying the given by splitting,
[tex]x^{2} + 4x + 4 = 0 \implies x^{2} + 2 x + 2x + 4\\\implies x(x+2) +2(x+2) =0\\or, (x+2)(x+2) = 0[/tex]
[tex]x = -2, x= -2[/tex]
Hence, for k= +4, the polynomial has two equal roots.
Now, let us assume the value of k = -4
So, the expression is [tex]x^{2} - 4x + 4 = 0[/tex]
Simplifying the given by splitting,
[tex]x^{2} - 4x + 4 = 0 \implies x^{2} - 2 x - 2x + 4\\\implies x(x-2) -2(x-2) =0\\or, (x-2)(x-2) = 0[/tex]
[tex]x = 2, x= 2[/tex]
Hence, for k = -4, the polynomial has two equal roots.
(3) Let us assume the value of k < -4
This gives us NO FIXED VALUE for k.
So, the expression is [tex]x^{2} + 4x + 4 = 0[/tex] can not be solved.
(4) let us assume the value of k > 4
This gives us NO FIXED VALUE for k.
So, the expression is [tex]x^{2} + 4x + 4 = 0[/tex] can not be solved.
Hence, for k =+4, and k = -4 the polynomial has two equal roots.
