Question

What is the value of the discrimination 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

The value is -4 but in there should be a square root sign around b^2 - 4ac and a there is no square root for a negative number so it has no real solutions

Explanation:

So a discriminant is when you plug your quadratic equation into √b^2-4ac to find out the amount of solutions you have. The formula for a quadratic equation is ax^2 + bx + c. So in this case, the equation is x^2 - 4x + 5 so b= - 4, a=1, and c=5. We plug it in now.

√(-4)^2 - 4 x (1) x (5)

Now we simplify

√16-20

√-4

There are rules to discriminants so if it is a positive number it has 2 solutions. If it is zero it has one. And if it is negative then it has none. In this case it is negative so it has none