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.