What is the discriminant of the equation x² − 2x + 13 = 0? Also, determine how many real solutions this equation has.

Correct option is B

Given:

Quadratic equation: $$x^2 - 2x + 13 = 0$$​​

Formula Used:
Discriminant D $$= b^2 - 4ac$$​ for $$ax^2 + bx + c = 0.$$​​

If D > 0: 2 distinct real roots

If D = 0: 1 real (repeated) root

If D < 0: 0 real roots (two non-real complex roots)

Solution:
Here a = 1, b = -2, c =13.
D $$= (-2)^2 - 4(1)(13) = 4 - 52 = -48.$$​​
Since D < 0, the equation has no real solutions (two complex conjugate solutions).