Answer:
Explanation:
To determine the nature of the roots of the quadratic equation 3x² - 4√3x + 4 = 0, we can use the discriminant. The discriminant (D) is calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.
Let's apply this formula to the given equation:
a = 3, b = -4√3, c = 4
D = (-4√3)² - 4(3)(4)
= 48 - 48
= 0
The discriminant is equal to 0.
Now, let's determine the nature of the roots based on the value of the discriminant:
1. If D > 0, the equation has two distinct real roots.
2. If D = 0, the equation has two identical real roots (also called a "double root").
3. If D < 0, the equation has two complex conjugate roots.
In this case, since the discriminant is 0, the equation has two identical real roots or a double root.
Therefore, the nature of the roots of the equation 3x² - 4√3x + 4 = 0 is that it has two identical real roots or a double root.