Question

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has? The discriminant is −4, so the equation has 2 real solutions. The discriminant is −4, so the equation has no real solutions. The discriminant is 35, so the equation has 2 real solutions. The discriminant is 35, so the equation has no real solutions.

Answer 1

Discriminant, D = b² - 4ac

x² - 4x + 5 = 0  comparing to  ax² + bx + c = 0

a = 1, b = -4, c = 5

D = b² - 4ac = (-4)² - 4*1*5 = 16 - 20 = -4

In taking the square root of the discriminant of -4, √-4 = 2i = Not Real. So:

Discriminant is -4, so the equation has no real roots.

The second option is correct.   

Answer 2

D = 16-20 = -4 

what mean exactly the second choice is right so the quadratic has no real solutions