The equation 2x2 + ax + b = 0 has only one solution. Given that a ≠ 0 and am = kb, then the relationship between k and m is

The equation 2x^2 + ax + b = 0 has only one solution. This means that the discriminant of the quadratic equation, which is given by a^2 - 4*b, must be equal to zero (since the discriminant gives the number of solutions of a quadratic equation).

So, we have:

a^2 - 4*b = 0

Given that a ≠ 0 and am = kb, we can substitute kb for a in the above equation:

(kb)^2 - 4b = 0 k^2 * b^2 - 4b = 0

We can factor out b:

b * (k^2 * b - 4) = 0

Since a ≠ 0, b ≠ 0. Therefore, the second factor must be zero:

k^2 * b - 4 = 0

Solving for k, we get:

k = ± sqrt(4/b)

So, the relationship between k and m is that k is equal to the positive or negative square root of 4 divided by b.