AnswersFL-1200330-Algebra 2 AThe Quadratic Formula

The Quadratic Formula Answers

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1
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If the discriminant of a quadratic equation is equal to , which statement describes the roots?

Question illustration
A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
2
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Which equation has the solutions ?

Question illustration
A
3x2 – 5x + 7 = 0
B
3x2 – 5x – 1 = 0
C
3x2 – 10x + 6 = 0
D
3x2 – 10x – 1 = 0
3

Which equation can be solved using the expression for x?

Question illustration
A
10x2 = 3x + 2
B
2 = 3x + 10x2
C
3x = 10x2 – 2
D
10x2 + 2 = –3x
4

What is the discriminant of ?

Question illustration
A
76
B
94
C
106
D
124
5

The graph of an equation with a negative discriminant always has which characteristic?

A
no x-intercept
B
no y-intercept
C
no maximum
D
no minimum
6

In the derivation of the quadratic formula by completing the square, the equation is created by forming a perfect square trinomial. What is the result of applying the square root property of equality to this equation?

Question illustration
A
mc032-2.jpg
Option A
B
mc032-3.jpg
Option B
C
mc032-4.jpg
Option C
D
mc032-5.jpg
Option D
7

Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?

A
x = StartFraction negative 1 plus-or-minus StartRoot (negative 1) squared minus 4 (7) (9) EndRoot Over 2 (7) EndFraction
Option A
B
x = StartFraction 1 plus-or-minus StartRoot (negative 1) squared minus 4 (7) (9) EndRoot Over 2 (7) EndFraction
Option B
C
x = StartFraction negative 1 plus-or-minus StartRoot (negative 1) squared +4 (7) (9) EndRoot Over 2 (7) EndFraction
Option C
D
x = StartFraction 1 plus-or-minus StartRoot (negative 1) squared +4 (7) (9) EndRoot Over 2 (7) EndFraction
Option D
8

If the discriminant of a quadratic equation is equal to , which statement describes the roots?

Question illustration
A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
9

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

A
The discriminant is negative.
B
The discriminant is –3.
C
The discriminant is 0.
D
The discriminant is positive.
10

The first two steps in the derivation of the quadratic formula by completing the square are shown below. Which answer choice shows the correct next step?Step 1: Step 2:

Question illustration
A
mc031-3.jpg
Option A
B
mc031-4.jpg
Option B
C
mc031-5.jpg
Option C
D
mc031-6.jpg
Option D
11

Which equation has the solutions ?

Question illustration
A
x2 + 2x + 4 = 0
B
x2 – 2x + 4 = 0
C
x2 + 2x – 4 = 0
D
x2 – 2x – 4 = 0
12

What is the discriminant of ?

Question illustration
A
76
B
94
C
106
D
124
13

What is the discriminant of 9x2 + 2 = 10x?

A
–356
B
–172
C
28
D
72
14

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

A
StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction
Option A
B
StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction
Option B
C
StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction
Option C
D
StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction
Option D

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