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