Quadratic Equations: Factoring and Extracting Square Roots

What is the first step in solving a quadratic equation by factoring?

• Divide by the coefficient of x^2

• Convert the equation to standard form

• Find the square root of each term

• Transpose all terms to one side

In the equation 4x^2 - 9 = 0, what are the factors when solved by factoring?

• (2x + 3)(2x - 3)

• (4x + 9)(4x - 9)

• (2x + 9)(2x - 9)

• (x + 3)(x - 3)

What is the pattern to follow when solving quadratic equations by extracting square roots?

• ax^2 - c = 0

• ax^2 + bx = c

• ax^2 = c

• ax^2 + bx + c = 0

When extracting square roots, what must you remember to include?

• Both positive and negative roots

• Only the negative root

• Only the positive root

• No roots

What is the solution to the equation x^2 - 100 = 0?

• x = 0

• x = ±10

• x = -10

• x = 10

How do you simplify the square root of 8?

• 2√2

• 8

• 4

• √4

What is the solution to the equation 9x^2 = 8?

• x = ±√(9/8)

• x = ±√(8/9)

• x = ±9/8

• x = ±8/9

What is the imaginary unit 'i' equivalent to?

• √1

• √-1

• √0

• √-25

What is the solution to the equation x^2 + 25 = 0?

• x = ±5

• x = ±i

• x = ±5i

• x = ±25

What happens when you take the square root of a negative number?

• It becomes undefined

• It becomes an imaginary number

• It becomes zero

• It becomes a positive number