1. Work with a partner to decide all values of b in the following equations that will give one or more real number solutions.

A. 3x^2 + bx-3= 0
B. 5x^2 + bx+1= 0
C. -3x^2 +bx-3= 0
D. Write a rule for judging if an equation has solutions by looking at it in standard form.

*What is your conclusion?*

2. Solve the following quadratic equations by factoring or by any of the techniques of this chapter using what you consider to be the optimum method for each problem. Share why you chose one method over the other for each problem.

A. (x - 1)^2 = 7
B. x^2 - 9x - 4 = 6
C. 4x^2 - 8x + 3 = 5

Solution Preview

Quadratic Equations

1. Work with a partner to decide all values of b in the following equations that will give one or more real numbers solutions.

A 3x^2 + bx-3= 0

Let's start by solving for x using the quadratic equation:

x = -b ± √[b^2 - 4(3)(-3)]
6

x = -b ± √[b^2 + 36]
6

We will have one or more real solutions (i.e. not imaginary ones) if the expression under the square root sign is either positive or equal to 0:

b^2 + 36 ≥ 0
b^2 ≥ -36

Answer: b can be any real number.

D Write a rule for judging if an equation has solutions by looking at it in standard form.

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