For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

If or , there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

This polynomial has roots such that , given by the following formulas:

The signal of determines how many real roots an equation has:

: Two real and different solutions

: One real solution

: No real solutions

In this problem, we have the following second order polynomial:

.

This means that

It has one solution if

We can simplify by 8

The solution is:

or

So, if or , there is only one solution to the given quadratic equation.