Question

What will be the value of "k" so that it will make it a perfect square?

Answer 1

Answer:

x²-8x+k

x²-4x-4x+k = x(x-4) -4(x-4) = (x-4)(x-4)

Perfect square = (x-4)(x-4) = x²-4x-4x+16 = x²-8x+16

k = 16

(i dont know the proper steps, hope it helps..)

Answer 2

Given,

$\[{x^2} - 8x + k\]$

Solution,

Know that $\[a{x^2} + bx + c\]$ will make perfect square if $\[{b^2} - 4ac = 0\]$

Compare the given equation with standard equation.

$\[a = 1,b = - 8,c = k\]$

$\[\begin{array}{l}{b^2} - 4ac = 0\\ \Rightarrow {( - 8)^2} - 4 \times 1 \times k = 0\\ \Rightarrow 4k = 64\\ \Rightarrow k = 16\end{array}\]$

Hence the value of k is 16.