Bluebook SAT Test Nonlinear Equations and Systems 6

Question 1

The product of two numbers is 40 and their sum is 13. Which quadratic equation has these two numbers as roots?

Accepted Answer

x² − 13x + 40 = 0

Answer

By Vieta's formulas: sum = 13 and product = 40 → x² − 13x + 40 = 0.

Question 2

What is the x-coordinate of the axis of symmetry of y = −2x² + 8x − 5?

Accepted Answer

x = 2

Answer

Axis of symmetry: x = −b/(2a) = −8 / (2·(−2)) = −8/(−4) = 2.

Question 3

The system y = 2x + k and y = x² has exactly one solution. What is k?

Accepted Answer

−1

Answer

x² = 2x + k → x² − 2x − k = 0; one solution when discriminant = 4 + 4k = 0 → k = −1.

Question 4

If 5x² = 45, what is the value of x²?

Accepted Answer

9

Answer

x² = 45 ÷ 5 = 9.

Question 5

Which of the following best describes the solutions of x² + 2x + 5 = 0?

Accepted Answer

No real solutions

Answer

Discriminant = 4 − 20 = −16 < 0, so there are no real solutions.

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