Question

Examine the quadratic equation: x^2+2x+1=0

Answer 1

Answer:

A: 0

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

Step-by-step explanation:

$\bf{x^2+2x+1=0}$

A:

The discriminant of the quadratic equation can be found by using the formula: $b^2-4ac$.

In this quadratic equation,

• a = 1
• b = 2
• c = 1

I found these values by looking at the coefficient of $x^2$ and $x$. Then I took the constant for the value of c.

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

• $b^2-4ac$
• $(2)^2-4(1)(1)$

Simplify this expression.

• $(2)^2-4(1)(1)= \bf{0}$

The answer for part A is $\boxed{0}$

B:

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

• Negative, there are no real solutions (two complex roots).
• Zero, there is one real solution.
• Positive, there are two real solutions.

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 $\boxed {\text{There is one real root with a multiplicity of 2.}}$

Answer 2

Answer:

A: 0  

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

Step-by-step explanation:

Given a quadratic equation:

 $ax^2+bx+c=0$

You can find the Discriminant with this formula:

$D=b^2-4ac$

In this case you have the following quadratic equation:

$x^2+2x+1=0$

Where:

$a=1\\b=2\\c=1$

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

$D=(2)^2-4(1)(1)\\\\D=0$

Since $D=0$, the quadratic equation has one real root with a multiplicity of 2 .