What are the possible values of n in the quadratic equation 2n² + 7n + 6 = 0?

To find the possible values of n in the quadratic equation 2n² + 7n + 6 = 0, we can use the quadratic formula:

n = (-b ± √(b² – 4ac)) / 2a

In this equation, a is the coefficient of n² (which is 2), b is the coefficient of n (which is 7), and c is the constant term (which is 6).

First, we need to calculate the discriminant:

b² – 4ac = 7² – 4(2)(6)

b² – 4ac = 49 – 48 = 1

Now that we have the discriminant, we can substitute a, b, and the discriminant into the quadratic formula:

n = (-7 ± √1) / (2 * 2)

This simplifies to:

n = (-7 ± 1) / 4

Next, we solve for the two possible values of n:

Therefore, the possible values of n in the quadratic equation 2n² + 7n + 6 = 0 are:

These values can be interpreted as the points where the parabola represented by the quadratic equation intersects the n-axis.