Determine the Nature of Roots of the Quadratic Equation 3x² − 2√6x + 2 = 0
Solution
Given: $$3x^2-2\sqrt{6}x+2=0$$
Here, $$a=3,\quad b=-2\sqrt{6},\quad c=2$$
Using the discriminant, $$D=b^2-4ac$$
$$D=(-2\sqrt{6})^2-4(3)(2)$$
$$D=24-24=0$$
Since $$D=0,$$ the roots are real and equal.
Answer
The equation 3x² − 2√6x + 2 = 0 has two real and equal roots.