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?

Answer 1

We have been given an equation $0 = x^2-4x + 5$. We are asked to find the discriminant of our given equation.    

We will use discriminant formula to solve our given problem.

$D=b^2-4ac$, where,

D = Discriminant,

b = Coefficient of x term,

a = Coefficient of $x^2$ term,

c = Constant.

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

$D=16-20$

$D=-4$

When D is less than 0, then equation has no real solutions.

When D is equal to 0, then equation one real solution.

When D is greater than 0, then equation has two real solutions.

Since $-4$ is less than 0, therefore, our given equation has no real solutions.