Completing the Square and Roots

What is the primary goal of completing the square in solving quadratic equations?

• To eliminate the constant term

• To transform the equation into a perfect square trinomial

• To find the vertex of the parabola

• To convert the equation into a linear form

When completing the square, what should be the leading coefficient of the quadratic term?

• Any positive number

• 2

• 1

• 0

Why is it important to consider both positive and negative roots when using the square root property?

• To simplify the equation

• To ensure the equation is balanced

• To find the maximum value of the function

• To obtain all possible solutions

What is the value of the imaginary unit 'i'?

• The square root of 2

• The square root of 0

• The square root of -1

• The square root of 1

What is the result of simplifying the square root of 45 divided by 81?

• The square root of 5 divided by 9

• The square root of 3 divided by 5

• The square root of 5 divided by 3

• The square root of 9 divided by 5

In the equation x^2 - 2x + 10 = 0, what number is added to both sides to complete the square?

• 9

• 4

• 0

• 1

How do you verify if a complex solution is correct?

• By checking the discriminant

• By using a calculator

• By substituting the solution back into the original equation

• By graphing the equation

What is the result of taking the square root of a negative number?

• A real number

• A complex number

• A rational number

• An integer

What is the first step in solving x^2 + 3x + 5 = 0 by completing the square?

• Subtract 3 from both sides

• Add 5 to both sides

• Isolate the variable terms

• Divide by 3

What is the final form of the equation x^2 + 2x + 3 = 0 after completing the square?

• (x + 2)^2 = -1

• (x - 1)^2 = 2

• (x - 2)^2 = 1

• (x + 1)^2 = -2