Question

Find the solutions to the equation below.

Check all that apply.
4x^2 - 3x + 3 = 0
A. X = 2
B. X = -2
C. x = -
D. X
E. X = 3

Answer 1

The quadratic equation 4x^2 - 3x + 3 = 0 has no real-number solutions, because the discriminant is negative. Therefore, none of the options provided are correct solutions.

Step-by-step explanation:

To find the solutions to the given quadratic equation 4x2 - 3x + 3 = 0, we can apply the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a) for any equation of the form ax2 + bx + c = 0. Plugging the values into the formula, where a = 4, b = -3, and c = 3, gives us:

x = (3 ± √((-3)2 - 4(4)(3))) / (2(4))

x = (3 ± √(9 - 48)) / 8

x = (3 ± √(-39)) / 8

Since the discriminant (b2 - 4ac) is negative (-39), this equation has no real-number solutions

Thus, none of the given options A, B, C, D, or E are correct solutions to the equation.