Question

Find the values of k for which the quadratic equation kx(x - 2) + 6 = 0 has two equal roots.

Answer 1

for two equal roots, b^2 - 4ac = 0

simplifying we get kx^2 - 2kx + 6 = 0
so a = k b = -2k and c = 6

so (-2k)^2 - 4 (k)(6) = 0
4k^2 - 24k = 0

what to do next...??

Answer 2

4k(k-6) = 0
k = 0 or k =6

Answer 3

But is k = 0 a valid solution ???

Answer 4

I think you might have become mixed up between the k's and the original equation in x.

for k = 0 and for k = 6, the original expression in terms of x has two equal solutions.

Answer 5

at least according to Coolsector... I think that's what he meant.

Answer 6

k = 0 doesn't look valid to me though.

Answer 7

kx(x - 2) + 6 = 0

for k = 6
(6)x(x-2) + 6 = 0
6x^2 - 12x + 6 = 0
6(x^2 - 2x + 1) = 0
(x-1)^2 = 0
two equal solutions are x = 1, x = 1

Answer 8

@JakeV8 is right about it ..
taking k = 0 wont do any good eventually
after finding k =0 or k =6
we need to go back and see what they really mean
k=0 mean 6=0 in the original equation

so the only possible value is k=6

Answer 9

yeah...that was my point...only 6 seems to be the valid solution here but the book said the values of k are 0 and 6 which is incorrect... Thanks guys for your time and effort....☺