Question

if 2/3 is the root of the equation kx^2-x-2=0 then find the value of k...

Answer 1

Substitute x = 2/3

K(2/3)² - 2/3-2 = 0
4k/9-2/3-2 = 0

(4k-6-18)/9 = 0
4k -24 = 0
K-6 = 0
K = 6

Answer 2

Hey there,
If a is the root of f(x) then f(a) = 0 .

Given f(x) = kx²-x-2

Here, 2/3 is the root,

So , f(2/3) = 0

k(2/3)²-(2/3)-2 = 0

k(4/9) -2/3 - 2 = 0

Multiply by 9

4k - 6 - 18 = 0

4k -24 = 0

k = 24/4 = 6 .

Hope helped !