Solving Quadratic Equations by Inspection

This lesson teaches how to solve quadratic equations by inspection. It begins with a review of perfect squares and the multiplication of square roots, highlighting common mistakes. The lesson then provides examples of solving quadratic equations, including those with perfect squares, non-perfect squares, and cases with no real solutions. Graphical interpretations of solutions are also discussed.

What is a perfect square?

• A number that is a multiple of 10

• A number that can be divided by 2

• A number that is the cube of an integer

• A number that is the square of an integer

Which of the following is a common mistake when dealing with square roots?

• Thinking that the square of a number is always negative

• Assuming the square root of a negative number is defined in the real number system

• Assuming that multiplying two square roots always results in a negative number

• Believing that the square root of a number is always an integer

If X^2 = 25, what are the possible values of X?

• 0 and 25

• 5 and -5

• Only -5

• Only 5

What is the graphical interpretation of the solutions to X^2 = 15?

• The graph has no X-intercepts

• The graph has one X-intercept at 15

• The graph is a straight line

• The graph has X-intercepts at sqrt(15) and -sqrt(15)

Why does the equation X^2 = -36 have no real solutions?

• Because -36 is a prime number

• Because the square of any real number is non-negative

• Because 36 is not a perfect square

• Because the equation is not quadratic