Question

In the following, find the value of k for which the given value is a solution of the given equation:

`7x^2 + kx - 3 = 0, x = 2/3`

Answer 1

We are given here that,

`7x^2 + kx - 3 = 0, x = 2/3`

Now, as we know that `x=2/3` is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting `x=2/3` in the above equation gives us,

7x² + kx - 3 = 0

`7(2/3)^2+k(2/3)-3=0`

`7(4/9)+(2k)/3-3=0`

`28/9+((2k)/3)-3=0`

`(2k)/3=3-28/9`

`(2k)/3=(27-28)/9`

`(2k)/3=(-1)/9`

`2k=(-1)/9xx3`

`2k=(-3)/9`

`k=((-3)/9)/2`

`k=(-3)/(9xx2)`

`k=(-3)/18`

`k=(-1)/6`

Hence, the value of `k=(-1)/6`.