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SAT数学:代数例题 10

2019-09-12 SAT-数学 阅读

SAT Question
Rank: Medium
Topic: Plane Geometry, Algebra, Factorizing Quadratics

Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 1-2 minutes to complete.

In the xy-plane, the graph of the function
has two x-intercepts. What is the distance between the x-intercepts?
(A)1
(B)2
(C)3
(D)4

This curve will the x-axis at the points where y=0. These are the x-intercepts.
So we will set our function equal to 0.

Now we have a quadratic equation which we can factorize.
We are looking for 2 numbers which add together to make 5 and multiply together to make 4.
Only 2 numbers satisfy these conditions. +4 and +1.
Therefore, we can place these numbers into double bracket form.

We can divide through by each bracket individually to get two solve able equations.
and
So, our solutions are:

Now we just need to find the difference between these numbers.

As a distance cannot be negative, we use the absolute value of 3.
So, the answer is C.

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