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Find the nature of the roots of 3x² -4√3x +4=0.

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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.

User Eduardo Bergel
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