# 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 intersects the graph of the equation *y* = *x*^{2} + *x* at two points. What is the distance between these two points?

- A.
- B.
- C.
- D. 4

**Correct Answer:** D

**Explanation:**

**D**

**Advanced Mathematics (polynomials) MEDIUM-HARD**

Given equation:

*y* = *x*^{2} + *x*

Substitute :

Multiply by 4:

15 = 4*x*^{2} + 4*x*

Subtract 15:

0 = 4*x*^{2} + 4*x* - 15

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

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

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

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

Solve each equation for *x*:

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

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