Question

equation has two equal roots, find the values of k...
x^2-6x+3=k(2^x-1)

Answer 1

If equation has to equal roots, the discriminant must be 0.

Answer 2

x^2 - 6x + 3 = kx^2-k

Answer 3

by the way is that a typo? 2^x?

Answer 4

typo- 2x ..not 2^x~

Answer 5

oh ok
so:
x^2-6x+3=2kx-k
x^2 - 6x - 2kx + 3+ k = 0

Answer 6

or grouping the terms or whatever u call that,
x^2 + (-6-2k)x + (3+k) = 0
Now for the equation to have two equal roots, the discriminant = b^2 - 4ac = 0.

Answer 7

b = -6-2k
a=1
c = 3+k
(-6-2k)^2 - 4 * 1 * (3+k) = (-6-2k)^2 - 12 - 4k = 0

Answer 8

((-1)*(6+2k))^2 - 12 - 4k = 0
(6+2k)^2 - 12 - 4k = 0
36 + 24k + 4k^2 - 12 - 4k = 0

Answer 9

4k^2 + 20k + 24 = 0
k^2 + 5k + 6 = 0

Answer 10

factoring that gets you:
(k+2)(k+3) = 0, so:
k = -2, or k = -3 will get u two equal roots