Evaluate the discriminant for the equation. Determine the number of real solutions.
4x^2+2x+4=0
The equation is given as 4x^2 + 2x + 4 = 0.
The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is calculated as D = b^2 - 4ac.
For the given equation:
a = 4,
b = 2,
c = 4.
D = (2)^2 - 4(4)(4)
= 4 - 64
= -60.
Since the discriminant (D) is negative (-60), the equation has no real solutions.