Question

The discriminant of the quadratic equation $3x^2 - 4\sqrt{3}\,x + 4 = 0$ will be:
 

• A. $4\sqrt{3}$
• B. $36$
• C. $0$
• D. $96$

Hint:

If the discriminant $D = 0$, the quadratic has real and equal roots. If $D > 0$, roots are real and distinct; if $D < 0$, roots are complex.

Answer 1

The Correct Option is C

Step 1: Recall the formula for discriminant
For a quadratic $ax^2 + bx + c = 0$: \[ D = b^2 - 4ac \]

Step 2: Identify coefficients
Here, $a = 3$, $b = -4\sqrt{3}$, $c = 4$.

Step 3: Substitute values
\[ D = (-4\sqrt{3})^2 - 4(3)(4) \] \[ = 16 \times 3 - 48 \] \[ = 48 - 48 = 0 \] \[ \boxed{D = 0} \]