Question

What value(s) of k would make `16x^2 -2/3kx+9` a perfect square trinomial?

Answer 1

We can say that a trinomial is a perfect square if it is in the form

`a^2x^2 + 2abxy + b^2y^2`

In the question, we want `16x^2 -2/3kx + 9` to be a perfect square trinomial

This means we can assume the following

`a^2 = 16`
`=> a = +-4`

`b^2 = 9`
`=> b = +- 3`

Since the coefficient of the second term is negative, either `a` or `b` should be negative.

Let's assume that `b` is negative.

`=> a = 4`
`=> b = -3`

`2ab = -2/3k`

`=> 2(4)(-3) = -2/3k`

`=> 4(-1 * 3) = -1/3k`

`=> 4*3 = 1/3k`

`=> 4*3*3 = k`

`=> 36 = k`

I will not show it anymore, but if we assume that `a` is negative, we should arrive at the same answer