Bluebook SAT Test Nonlinear Equations and Systems 1

Question 1

What are the solutions to x² − 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

x = −2 and x = −3

Answer

x = 1 and x = 6

Answer

x = −1 and x = −6

Question 2

The quadratic equation x² − 4x + k = 0 has exactly one real solution. What is the value of k?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 3

Which of the following are both solutions to 2x² + 3x − 2 = 0?

Accepted Answer

x = 1/2 and x = −2

Answer

x = 2 and x = −1/2

Answer

x = 1 and x = −2

Answer

x = 1/2 and x = 2

Question 4

How many real solutions does the equation x² + 6x + 10 = 0 have?

Accepted Answer

None

Answer

Exactly one

Answer

Exactly two

Answer

Infinitely many

Question 5

What is the vertex of the parabola y = x² − 8x + 15?

Accepted Answer

(4, −1)

Answer

(4, 1)

Answer

(−4, −1)

Answer

(−4, 1)

Question 6

Solve for x: x² = 49

Accepted Answer

x = 7 or x = −7

Answer

x = 7 only

Answer

x = −7 only

Answer

No real solution

Question 7

The parabola y = x² + bx + c passes through (0, 5) and (5, 0). What is the value of b?

Accepted Answer

−6

Answer

−5

Answer

−4

Answer

−3