Exam 9: Quadratic Equations

Solve the quadratic equation. Use whatever method seems to fit the situation or is convenient for you.

Solve the following equation by first multiplying both sides by the LCD and then applying the quadratic formula to the result.

Solve the equation.

Combine the complex numbers.

Graph the equation. Begin by completing the square on the first two terms.

Multiply the complex numbers.

Solve the equation using the square root method.

If one solution to a quadratic equation is what do you think the other solution is?

Multiply the complex numbers.

Solve the equation by first factoring out the common factor y and then using the quadratic formula.

Solve the equation.

Solve the equation by completing the square.

Combine the complex numbers.

An advertisement for a portable computer indicates it has a 17-inch viewing screen. This means that the diagonal of the screen measures 17 inches. If the ratio of the height to the width of the screen is 3 to 4, we can represent the height with 3 x and the width with 4 x , and then use the Pythagorean theorem to solve for x . Once we have x , the height will be 3 x and the width will be 4 x . Find the height and width of this computer screen to the nearest tenth of an inch.

If you invest in an account with interest rate compounded annually, the amount of money in the account after years is given by the formula .

Solve the equation using the square root method.

Solve the equation by using the quadratic formula.

Combine the complex numbers.

A company wants to know what price they should charge to make the maximum profit on their inexpensive digital watches. They have discovered that if they sell the watches for $1, they can sell 7 million of them, but if they sell them for $2, they can only sell 6 million. Let x be the number of million watches sold at p dollars per watch. Assume that the relationship between x and p is linear and find an equation that gives that relationship. Remember that revenue is price times number of items sold: R = xp . Solve the equation from the previous part for x and substitute the result into the equation R = xp in place of x ( R is in million of dollars). Graph the equation from previous part on a coordinate system where the horizontal axis is the p -axis and the vertical axis is the R -axis. The highest point on the graph will give you the maximum revenue. What is the maximum revenue?

Solve the equation.