SAT Math Multiple Choice Question 641: Answer and Explanation

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Question: 641

11. In the xy-plane, the graph of the line Images intersects the graph of the equation y = x2 + x at two points. What is the distance between these two points?

  • A. Images
  • B. Images
  • C. Images
  • D. 4

Correct Answer: D

Explanation:

D

Advanced Mathematics (polynomials) MEDIUM-HARD

Given equation:

y = x2 + x

Substitute images :

images

Multiply by 4:

15 = 4x2 + 4x

Subtract 15:

0 = 4x2 + 4x - 15

Factor using the Product-Sum Method (Chapter 9, Lesson 4):

0 = (2x + 5)(2x - 3)

Use Zero Product Property (Chapter 9, Lesson 5):

2x + 5 = 0; 2x - 3 = 0

Solve each equation for x:

x = -5/2; x = 3/2

Therefore, the two points of intersection are images and images, and the distance between these points is images

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