For what value of k does the equation (2k+1)x^2+2x=10x-6 have two real and equal roots?

Step-by-step explanation:

We are given the equation:

And we want to find the value of k 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:

First, rewrite our equation:

The discriminant is given by:

In this case, b = -8, a = (2k + 1), and c = 6.

Therefore, the discriminant is given by:

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

Solve for k:

Hence, the value of k is 5/6.

step-by-step explanation:

8/k

step-by-step explanation: