Bluebook SAT Test Nonlinear Equations and Systems 3

Question 1

Which of the following is equivalent to x² − 16?

Accepted Answer

(x − 4)(x + 4)

Answer

x² − 16 is a difference of squares: (x−4)(x+4).

Question 2

What is the positive solution of 3x² − 27 = 0?

Accepted Answer

x = 3

Answer

3x² = 27 → x² = 9 → x = ±3; the positive solution is x = 3.

Question 3

If (x − 3)² = 25, what are the possible values of x?

Accepted Answer

x = 8 or x = −2

Answer

x − 3 = ±5 → x = 8 or x = −2.

Question 4

Which quadratic has roots at x = −1 and x = 5?

Accepted Answer

x² − 4x − 5

Answer

Using factor form: (x+1)(x−5) = x² − 4x − 5.

Question 5

How many real solutions does x² + 4 = 0 have?

Accepted Answer

None

Answer

x² = −4 has no real solutions since a square cannot be negative.

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