Question

Determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve.

62x² - 2 = 0
A. Discriminant = 0, One real solution
B. Discriminant > 0, Two real solutions
C. Discriminant < 0, Two complex solutions
D. Discriminant = 0, Two equal real solutions

Answer 1

The B) discriminant is positive, indicating two real solutions. The solutions are not equal.

Step-by-step explanation:

To determine the discriminant, we will use the formula D = b²- 4ac. In the given quadratic equation 62x²-2=0, the values of a, b, and c are 62, 0, and -2 respectively. Plugging these values into the discriminant formula, we get D = (0)²- 4(62)(-2) = 0-(-496) = 496.

Since the discriminant is positive (D > 0), there are two real solutions. The nature of the solutions can be determined by looking at the discriminant's value. Since the discriminant is not equal to 0, the solutions are not equal. Therefore, the