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

in a quadratic equation
b=-4
a=1
c=5
discriminant=b^2-4ac
=-4^2-4*1*5
=16-20
=-4

Answer 2

Given:

0 = x² − 4x + 5

To Find:

The discriminant

Recall:

$\boxed{\\\begin{minipage} {7 cm}\\\\\\\text{Discriminant is greater than zero}\\\implies\text{there are 2 real solutions}\\ \text{Discriminant is equal zero}\\\implies\text{there is 1 solution}\\\text{Discriminant is less than zero}\\\implies\text{there is no real solution} \\\end{minipage}}$

Solution

Find the discrimination:

$x^2 - 4x + 5$

$\implies a = 1, b = -4, c = 5$

$D = b^2 - 4ac$

$D = (-4)^2 - 4(1)(5)$

$D = 16 - 20$

$D = -4$

Conclusion:

$\text{Discriminant} = -4$

$\implies \text{There is no real solution}$

$\boxed{\textbf{ Answer: The discriminant is -4, so the equation has no real solutions.}}$