Question

Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation one-halfx2 + 4x + 8 = 0. Which explanation could Anderson provide?

The equation has no real number solutions because the discriminant is 0.
The equation has one real number solution because the discriminant is 0.
The equation has no real number solutions because the discriminant is less than 0.
The equation has two real number solutions because the discriminant is greater than 0.

Answer 1

The equation has one real number solution because the discriminant is 0.

Explanation:

• If the discriminant is less than 0, there are no real number solutions.
• If the discriminant is equal to 0, there is one real number solution.
• If the discriminant is greater than 0, there are two real number solutions.

Formula: D =
`b^(2)` - 4ac

`(1)/(2) x^(2)+4x+8=0`

⇒ a = 1/2, b = 4, c = 8

⇒ D = 4*4 - 4*0.5*8 = 16 - 16 = 0

⇒ The equation has one real number solution because the discriminant is 0.