Bluebook SAT Test Nonlinear Equations and Systems 14

Question 1

If 3x² − 75 = 0, what are the solutions for x?

Accepted Answer

x = ±5

Answer

3x² = 75 → x² = 25 → x = ±5.

Question 2

The system y = x² and y = 3x − 2 intersects at two points. What is the larger x-value?

Accepted Answer

x = 2

Answer

x² = 3x − 2 → x² − 3x + 2 = 0 → (x − 1)(x − 2) = 0; larger x = 2.

Question 3

For what positive value of x does x² − 5x + 4 = 0?

Accepted Answer

x = 1 and x = 4 (both positive)

Answer

(x − 1)(x − 4) = 0; both x = 1 and x = 4 are positive solutions.

Question 4

A parabola opens downward and has x-intercepts at x = −1 and x = 5. Which equation could model this parabola?

Accepted Answer

y = −(x + 1)(x − 5)

Answer

x-intercepts at −1 and 5 give factors (x + 1)(x − 5); downward opening requires a negative leading coefficient: y = −(x + 1)(x − 5).

Question 5

The roots of x² − 8x + 15 = 0 are p and q. What is the value of p² + q²?

Accepted Answer

34

Answer

p + q = 8; pq = 15; p² + q² = (p + q)² − 2pq = 64 − 30 = 34.

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