In the equation x squared -2x + k = 0, one root is 6 a) find the other root b) find the value of k?

Answer 1

Replace x with 6
6^2 - 2(6) + k = 0
36 - 12 + k = 0
24 + k = 0
k = -24
The other root is -24/6 = -4

Answer 2

x^2-2x+k=0
6^2-2(6)+k=0 or 36-12+k=0 or k= -24

so now x^2-2x-24=0
x^2-6x+4x-(6)(4) =0 middle term factorization process
x(x-6) +4(x-6) =0 by taking common
(x-6)(x+4)=0
so either x-6=0 or x=6 (given)
or x+4=0 or x= -4 the other root

Answer 3

Using Synthetic Division, since 6 and k are roots, when dividing the polynomial by (x-6), we should get a remainder of 0::
6 | -2 k
. . . -12
----------------
. . -2 . k-12
k - 12 = 0
k = 12
-2x +12 = 0
-2*(x - 6) = 0 [Check]

Answer 4

x^2 - 2x + k = 0
(x - 6)(x - a) or (x - 6)(x + a)
x^2 - ax - 6x + 6a or x^2 + ax - 6x - 6a

(-a - 6)x = -2x
-a - 6 = -2
-a = 4
a = -4

k = 6(-4) = -24

or

(a - 6)x = -2x
a - 6 = -2
a = 4

k = 6(4) = 24

(x - 6)(x + 4) or (x - 6)(x - 4)
(x^2 + 4x - 6x - 24) or (x^2 - 4x - 6x + 24)
x^2 - 2x - 24 or x^2 - 10x + 24

The only one that fits is (x - 6)(x + 4) = x^2 - 2x - 24

ANS :
a.) -4
b.) -24