Second Degree Equations

Question 1

What is a second degree equation?

Accepted Answer

An equation in which the unknown appears squared and no higher power, e.g. x^2 + 2x = 224 or x^2 - 4x + 3 = 0.

Question 2

Solve x^2 = 25.

Accepted Answer

x = \pm 5. Remember both the positive and negative roots: x = 5 or x = -5.

Question 3

What is 'completing the square'?

Accepted Answer

Rewriting x^2 + bx as \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2, so the equation can be solved by taking a square root.

Question 4

For x^2 + 6x = 7, what do you add to complete the square?

Accepted Answer

Add \left(\frac{6}{2}\right)^2 = 9 to both sides, giving (x+3)^2 = 16.

Question 5

Common mistake: forgetting the \pm when taking a square root.

Accepted Answer

x^2 = 9 has two answers, x = 3 and x = -3. Always write \pm when you square-root both sides.

Sample questions