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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

Respuesta :

Supernova

Answer:

A: 0

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

Step-by-step explanation:

[tex]\bf{x^2+2x+1=0}[/tex]

A:

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

In this quadratic equation,

  • a = 1
  • b = 2
  • c = 1

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

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

  • [tex]b^2-4ac[/tex]
  • [tex](2)^2-4(1)(1)[/tex]

Simplify this expression.

  • [tex](2)^2-4(1)(1)= \bf{0}[/tex]

The answer for part A is [tex]\boxed{0}[/tex]

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 [tex]\boxed {\text{There is one real root with a multiplicity of 2.}}[/tex]

luisejr77

Answer:

A: 0  

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

Step-by-step explanation:

Given a quadratic equation:

 [tex]ax^2+bx+c=0[/tex]

You can find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

In this case you have the following quadratic equation:

[tex]x^2+2x+1=0 [/tex]

Where:

[tex]a=1\\b=2\\c=1[/tex]

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

[tex]D=(2)^2-4(1)(1)\\\\D=0[/tex]

Since [tex]D=0[/tex], the quadratic equation has one real root with a multiplicity of 2 .