What is the nature of the roots of the quadratic equation x² – 5x + 7 = 0 ?

Correct option is B

Given:

Quadratic equation: x² – 5x + 7 = 0 

Concept Used:  

D>0: When D is positive, the equation will have two real and distinct roots. This means the graph of the equation will intersect x-axis at exactly two different points.

D < 0: When D is negative, the equation will have no real roots roots are imaginary . This means the graph of the equation will not intersect x-axis.

Formula Used:

The nature of the roots of a quadratic equation is determined by the discriminant (D):

D = b² - 4ac

For the equation x² – 5x + 7 = 0, coefficients are:

a = 1, b = -5, c = 7

Solution:

Calculate the discriminant (D).

D = b² - 4ac

= (-5)² - 4(1)(7)

= 25 - 28

= -3

Determine the nature of the roots based on D.

D < 0:  D is negative, the equation will have no real roots roots are imaginary (not real) . This means the graph of the equation will not intersect x-axis.​