Determine the Nature of Roots of the Quadratic Equation 2x² − 3x + 5 = 0
Solution
Given: $$2x^2-3x+5=0$$
Here, $$a=2,\quad b=-3,\quad c=5$$
Using the discriminant, $$D=b^2-4ac$$
$$D=(-3)^2-4(2)(5)$$
$$D=9-40=-31$$
Since $$D<0,$$ the roots are imaginary (non-real) and distinct.
Answer
The equation 2x² − 3x + 5 = 0 has two distinct imaginary (non-real) roots.