Solving Quadratic Equations by Extracting the Square Root

All quadratic equations can be solved by factoring.

• True

• False

Answer explanation

Not all quadratic equations can be solved by factoring, some may require other methods like the quadratic formula or completing the square.

What appropriate method of solving can we used in the equations that are written in the form x² = c?

• factoring

• quadratic formula

• extracting square roots

• completing the square

Answer explanation

The appropriate method of solving equations in the form x^2 = c is by extracting square roots.

Which of the following quadratic equations can be solved easily by extracting the square root?

• x² - 4 = 0

• x² - 4x = 0

• x² + 4x - 4 = 0

• x² - 4x - 4 = 0

Answer explanation

The quadratic equation x^2 - 4 = 0 can be easily solved by extracting the square root to find x = ±2, making it the correct choice.

Find the solutions of the equation x² - 16 = 0 by extracting the square root.

• x = 4 and x = -4

• x = 4

• x = -4

• no answer

Answer explanation

To solve x^2 - 16 = 0 by extracting the square root, we get x = ±√16, which gives x = ±4. Therefore, the solutions are x = 4 and x = -4.

Which of the following quadratic equations can be solved by extracting square roots?

• x² + 3x – 4 = 0

• 2x² – 50 = 0

• (x + 1) (x – 3)

• 2x² – 5x – 7 = 0

Answer explanation

The quadratic equation x^2 - 36 = 0 can be solved by extracting square roots to get x = ±6, which is the correct choice.

What equation has the roots of x = 7 and x = -7?

• x² - 14 = 0

• x² - 49 = 0

• x² + 49 = 0

• x² = 14

Answer explanation

The correct equation is x^2 - 49 = 0 because the roots are 7 and -7, which are the square roots of 49 with opposite signs.

Which of the quadratic equations below can be solved easily be extracting the square root?

• 3x² + 9x = 0

• 2x² + 5x + 3 = 0

• x² – 2x + 1 = 0  

• 4x² – 16 = 0

Answer explanation

The quadratic equation 4x^2 - 16 = 0 can be easily solved by extracting the square root to get x^2 = 4, and then solving for x.

What are the roots of the quadratic equation 3t² = 12?

• t =4 and t = -4

• t = 2 and t = -2

• t = 3 and t = -3

• t = 9 and t = -9

Answer explanation

The roots of the quadratic equation 3t^2 = 12 are t = 2 and t = -2, as when solving for t, we get t = ±√(12/3) = ±√4 = ±2.

Answer explanation

The correct solutions to the equation x^2-81=0 are ±9, as when 81 is added or subtracted from 0, the result is 81 or -81 respectively.

Answer explanation

The roots of the equation are found by setting the equation equal to zero and solving for x. In this case, 2x^2 - 32 = 0 simplifies to x = ±4, giving the correct answer choices.