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.

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.

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abidemiokin abidemiokin · Answer 2 · 2022-04-13T10:47:36+02:00

The discriminant is −4, so the equation has no real solutions

Discriminant of a quadratic equation

The discriminant is used to determine the nature of a quadratic equation

Given the quadratic equation

0 = x2 − 4x + 5

From the equation

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

Substitute

D = (-4)^2 - 4(1)(5)
D = 16 - 20

D = -4

Since the discriminant is −4, so the equation has no real solutions

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