Question

Which equation has exactly ONE solution?

A) 3 + 10x² = 4x + 2
B) 15x − 5/3 = 5x + 4
C) 2 + 6x² = 3x + 1
D) 4x − 10/2 = 2x − 5

Answer 1

The equation that has exactly one solution is option A) 3 + 10x² = 4x + 2.

Step-by-step explanation:

The equation that has exactly one solution is option A) 3 + 10x² = 4x + 2.

To determine this, we can simplify the equation and check its discriminant. Rearranging the equation, we get 10x² - 4x = -1, or 10x² - 4x + 1 = 0.

The discriminant is given by b² - 4ac, where a = 10, b = -4, and c = 1. Plugging these values into the formula, we get (-4)² - 4(10)(1) = 16 - 40 = -24.

Since the discriminant is negative, the equation has exactly one solution. Therefore, option A) is the correct answer.