The equation has one real number solution because the discriminant is 0.
Step-by-step 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 = [tex]b^{2}[/tex] - 4ac
[tex]\frac{1}{2} x^{2}+4x+8=0[/tex]
⇒ 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.