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46. The correct answer is (A). [0] The Quadratic Formula:
is used to find the roots of a quadratic equation having the form ax
2
+ bx + c. b
2
– 4ac is called the
discriminant because it discriminates among three possibilities:
(1) When b
2
– 4ac = 0, the equation has two equal real roots.
(2) When b
2
– 4ac > 0, the equation has two unequal real roots.
(3) When b
2
– 4ac < 0, the equation has no real roots.
Therefore, for the equation given in the question stem, ax
2
+ bx + c = 0 has only one solution. The
graph given in choice (A) is the only one that has only one point on the x axis (where y = 0).

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Lesson 8
246
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ARCO
■ SAT II Subject Tests
47. The correct answer is (B). The plane cuts the cube in this way:
The smaller fragment has four sides: three right isosceles triangles with sides of 1 and an equilateral
triangle with sides equal to the diagonal of the face of the cube. So we need only find the areas of
those triangles and add in order to find the surface area of the smaller fragment.
The area of the three right isosceles triangles is:
(Or you might just see that their area is half that of the face of the cube, and 1/2 of 1 = 1/2.) And since
there are three of them:
The sides of the equilateral triangle are diagonals of faces of the cube.
To find the area of the equilateral triangle, we need an altitude:
Using the properties of the 30–60–90 triangle, we determine the length of the altitude:
Side opposite 60
° angle = 
1
2
× hypotenuse × 
Alt
= ×
×
=
1
2
2
3
6
2

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