Determine the Nature of Roots of the Quadratic Equation 2x² − 6x + 3 = 0
Solution
Given: $$2x^2-6x+3=0$$
Here, $$a=2,\quad b=-6,\quad c=3$$
Using the discriminant, $$D=b^2-4ac$$
$$D=(-6)^2-4(2)(3)$$
$$D=36-24=12$$
Since $$D>0,$$ the roots are real and distinct.
Answer
The equation 2x² − 6x + 3 = 0 has two distinct real roots.