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

A quadratic equation that has 2 roots that are equal means that the discriminant  of the equation is 0. The value of k that makes the equation have 2 real and equal roots is

Given that:

Rewrite as:

A quadratic equation is represented as:

By comparison:

If an equation has 2 real and equal roots, then:

So, we have:

Divide by 4

Divide by 6

Subtract 2 from both sides

Take LCM

Divide by 2

Hence, the value of k that makes the equation have 2 real and equal roots is

Read more about real and equal roots at:

step-by-step explanation:

b and c