Question

If the quadratic equation kx^2 + 8x + 2 = 0 has exactly one solution, what is the value of k?

a) k = 16
b) k = 8
c) k = 4
d) k = 2

Answer 1

For the quadratic equation kx^2 + 8x + 2 = 0 to have exactly one solution, the discriminant must be zero. Thus, solving 8^2 - 4(k)(2) = 0 gives us k = 8.

Step-by-step explanation:

To determine the value of k for the quadratic equation kx^2 + 8x + 2 = 0, that has exactly one solution, we rely on the concept of the discriminant in the quadratic formula. The quadratic formula for solving ax^2 + bx + c = 0 is given by x = (-b ± √(b^2 - 4ac)) / (2a). A quadratic equation has exactly one solution when the discriminant (the expression under the square root, b^2 - 4ac) is equal to zero. Hence, we set up the equation 8^2 - 4(k)(2) = 0.

Solving for k, we get:

• 64 - 8k = 0
• 8k = 64
• k = 8

Thus, the value of k is 8, which is option b.