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: βˆ’3 B: There is one real root with a multiplicity of 2 . B: There are two real roots. B: There are two complex roots

Accepted Solution

Answer:A: 0B: 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 = 1b = 2c = 1I 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 isNegative, 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]