Question

tell me fast... with full explanation i will mark u as brainlist .... write in paper​

Answer 1

Answer:

Since, it is given that the equation has equal roots.....

b^2 - 4ac=0

$kx(x - 2) + 6 = 0$

$kx {}^{2} - 2kx + 6 = 0$

$( - 2k) {}^{2} - 4(k)(6) = 0$

$4k {}^{2} - 24k = 0$

$4k(k - 6) = 0$

$either$

$k = 0$

$or$

$k = 6$

Answer 2

$\bf\huge{ \color{grey}answer}$

We have,

$\bf \: kx(x - 2) + 6 = 0 \\ \ \ \bf \: k {x}^{2} - 2kx + 6 = 0$

Comparing with

$\small{ \tt \: a {x}^{2} + bx + c = 0}$

We get,

a = k ; b = -2k ; c = 6

putting values in

$\tt \: {b}^{2} - 4ac = 0$

Because we have to find value of k for equal roots.

So,

$\bf \: {( - 2k)}^{2} - 4(k)(6) = 0 \\ \\ \bf \: 4 {k}^{2} - 24k = 0 \\ \\ \bf \: k(4k - 24) = 0 \\ \\ \bf \: 4k = 24 \\ \\ \boxed{ \bf{ \: k = 6}}$

Therefore, Value of k is 6.