Bluebook SAT Test Nonlinear Equations and Systems 7

Question 1

A quadratic equation has roots x = 2 + √3 and x = 2 − √3. What is the quadratic equation?

Accepted Answer

x² − 4x + 1 = 0

Answer

Sum = 4, product = (2)² − (√3)² = 4 − 3 = 1; equation: x² − 4x + 1 = 0.

Question 2

The height of a projectile is modeled by h = −5t² + 20t + 60. At what positive time t does the projectile hit the ground (h = 0)?

Accepted Answer

t = 6 only

Answer

−5t² + 20t + 60 = 0 → t² − 4t − 12 = 0 → (t−6)(t+2) = 0 → t = 6 (positive) or t = −2 (rejected).

Question 3

If 2x² − 8 = 0, what are the solutions for x?

Accepted Answer

x = ±2

Answer

2x² = 8 → x² = 4 → x = ±2.

Question 4

The system y = x² − x − 6 and y = 2 is solved. What is the sum of the x-coordinates of the intersection points?

Accepted Answer

1

Answer

x² − x − 6 = 2 → x² − x − 8 = 0; by Vieta's formulas, sum of roots = −(−1)/1 = 1.

Question 5

What value of c makes x² + 10x + c a perfect square trinomial?

Accepted Answer

25

Answer

For a perfect square: c = (b/2)² = (10/2)² = 25.

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