Question

Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation 1/2x2 + 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

Answer:

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

Step-by-step explanation:

The given quadratic equation y = 1/2x^2 + 4x + 8

Here a = 1/2, b = 4 and c = 8

discriminant d = b^2 - 4ac

d = (4)^2 - 4*1/2*8

d = 16 - 2* 8

d = 16 - 16

d = 0

If the discriminant is 0, there is one real number solution.

Therefore, answer is b) The equation has one real number solution because the discriminant is 0.

Hope this will helpful.

Thank you.

Answer 2

Let's actually solve this problem:

1/2x2 + 4x + 8 = 0 has coefficients  a = 1/2, b = 4 and  c = 8

Thus, the discriminant is   b^2 - 4ac, or (4)^2 - 4(1/2)(8)  =  16 - 16 = 0

When the discriminant is zero, as it is here, the quadratic equation has two real, equal roots (solutions).