Question

for what value of k the quadratic eqstn kx square -8x+k=0 has equal roots​

Answer 1

Answer:

$\green{k=4}$

Step-by-step explanation:

$\boxed{Given}$

The quadratic equation

$\underline{kx^2-8x+k}$

has equal roots

$\boxed{Tofind}$

value of k

$\blue{Answer}$

If the quadratic equation

$\underline{kx^2-8x+k}$

has equal roots then the discriminant

is equal to 0

That is

$b {}^{2} - 4ac = 0 \: for \: equal \: roots$

$\boxed{b=-8}$

$\boxed{a=k}$

$\boxed{c=k}$

putting the value we get

$( - 8) {}^{2} - 4(k)(k) = 0$

$64 - 4k {}^{2} = 0$

$- 4k {}^{2} = - 64$

$k { }^{2} = \frac{ - 64}{ - 4}$

$k {}^{2} = 16$

$k = \sqrt{16}$

$k = 4$