Examine the quadratic equation: x^2+2x+1=0
a: what is the discriminant of the quadratic equation?
b: based on the discriminant, which statement about the roots of the quadratic equation is correct?
select one answer choice for question a, and select one answer choice for question b.
a: 3
a: 0
a: −3
b: there is one real root with a multiplicity of 2 .
b: there are two real roots.
b: there are two complex roots

A: 0

B: There is one real root with a multiplicity of 2.

Step-by-step explanation:

The discriminant of the quadratic equation can be found by using the formula: .

In this quadratic equation,

I found these values by looking at the coefficient of and . Then I took the constant for the value of c.

Substitute the corresponding values into the formula for finding the discriminant.

Simplify this expression.

The answer for part A is

The discriminant tells us how many real solutions a quadratic equation has. If the discriminant is

Since the discriminant is 0, there is one real root so that means that the first option is correct.

The answer for part B is

A: 0  

B: There is one real root with a multiplicity of 2 .  

Step-by-step explanation:

Given a quadratic equation:

You can find the Discriminant with this formula:

In this case you have the following quadratic equation:

Where:

Therefore, when you substitute these values into the formula, you get that the discriminant is this:

Since , the quadratic equation has one real root with a multiplicity of 2 .

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