Question

If Kx(x-2)-6=0(k is not equal to 0)have two equal roots find the value of K​

Answer 1

${\boxed{\underline{\tt{\orange{Required \: Answer:-}}}}}$

◉GIVEN:-

Quadratic equation:- kx( x-2)+6=0

(kx^2 - 2kx + 6 = 0)

◉TO FIND:-

Value of K

◉FORMULA USED:-

b^2 - 4ac = 0 (because this quadratic equation have two equal roots)

◉SOLUTIONS:-

Comparing the given equation with general equation ax^2 + bx + c = 0

We get,

a = k

b = -2k

c = 6

$: \longrightarrow \sf{( { - 2k)}^{2} - 4(k)(6) = 0} \\ \\ : \longrightarrow \sf{4 {k}^{2} - 24k = 0 } \\ \\ : \longrightarrow \sf{4k(k - 6) = 0} \\ \\ \sf{ \therefore \pink{ \: k = 0 \: and \: k = 6}}$

HOPE IT HELPS :)