Answer:
[tex]k = 4[/tex]
Step-by-step explanation:
Given
[tex]4x^2 - 8x + k[/tex]
Required
Determine k if the expression is a perfect square
A quadratic is of the form;
[tex]ax^2 + bx + c[/tex]
Where (by comparison):
[tex]a = 4[/tex] [tex]b = 8[/tex] [tex]c = k[/tex]
If the above is a perfect square, then
[tex]k = \frac{b^2}{4a}[/tex]
Substitute values for a, b and c
[tex]k = \frac{8^2}{4*4}[/tex]
[tex]k = \frac{64}{16}[/tex]
[tex]k = 4[/tex]
Hence, k = 4
