Question

Find the nature of roots of the equation \(3x^2 - 4\sqrt{3}x + 4 = 0\).

Answer 1

Quadratic Equation: Root Characteristics

The quadratic equation provided is:

\[ 3x^2 - 4\sqrt{3}x + 4 = 0 \]

This equation is in the form \( ax^2 + bx + c = 0 \), where:

• \( a = 3 \)
• \( b = -4\sqrt{3} \)
• \( c = 4 \)

Step 1: Compute the Discriminant

\[ D = b^2 - 4ac = (-4\sqrt{3})^2 - 4(3)(4) \] \[ = (16)(3) - 48 = 48 - 48 = 0 \]

Step 2: Determine Root Type

Because \( D = 0 \), the quadratic equation possesses: Real and Equal Roots.

✅ Conclusion: The roots are real and identical.