Determine the Nature of Roots of the Quadratic Equation 3x² − 4√3x + 4 = 0
Solution
Given: $$3x^2-4\sqrt{3}x+4=0$$
Here, $$a=3,\quad b=-4\sqrt{3},\quad c=4$$
Using the discriminant, $$D=b^2-4ac$$
$$D=(-4\sqrt{3})^2-4(3)(4)$$
$$D=48-48=0$$
Since $$D=0,$$ the roots are real and equal.
Answer
The equation 3x² − 4√3x + 4 = 0 has two real and equal roots.