Question

Find all values of k for which the equation has one real solution.

(k - 4)w² - 3w + 2 = 0
Write your answer starting with k, followed by an equals sign or inequality symbol

Answer 1

`k=(41)/(8)`

Explanation:

the quadratic equation
`ax^2+bc+c=0` has one real solution if its discriminant is equal to zero, it means if
`b^2-4ac=0`.

In our case, we would have that

`a=k-4, b=-3, c=2`

Then:

`(-3)^2-4(k-4)(2)=0\\9-8(k-4)=0\\9-8k+32=0\\-8k+41=0\\k=(-41)/(-8)=(41)/(8)`