Answer:

Step-by-step explanation:
We are given the equation: 

And we want to find the value of <em>k</em> such that the equation has two real and equivalent roots. 
Since the equation is a quadartic, we can find its discriminant (symbolized by Δ). Recall that: 
- If Δ < 0, we have no real roots (two complex roots). 
- If Δ > 0, we have two real roots. 
- And if Δ = 0, we have one real root, or two equivalent ones. 
First, rewrite our equation: 

The discriminant is given by: 

In this case, <em>b</em> = -8, <em>a</em> = (2<em>k</em> + 1), and <em>c</em> = 6. 
Therefore, the discriminant is given by: 

For it to have two equal roots, the discriminant must be zero. Hence: 

Solve for <em>k: </em>
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Hence, the value of <em>k</em> is 5/6.