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Solving Quadratic Equations: Quadratic Formula Answers

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A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?

A
-1
B
0
C
1
D
2
2
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What is the positive solution to the equation 0 = –x2 + 2x + 1?Quadratic formula: x =

Question illustration
A
–2 +
Option A
B
2 –
Option B
C
1 +
Option C
D
–1 +
Option D
3

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?Quadratic formula: x =

Question illustration
A
x = 5
Option A
B
x = 5
Option B
C
x = 5
Option C
D
x = 5
Option D
4

What is the discriminant of the quadratic equation 3 – 4x = –6x2?

A
–68
B
–56
C
76
D
88
5

What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?

A
–4
B
8
C
12
D
24
6

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 7x + 4 has. Which best describes the discriminant and the number of zeros?

A
The equation has one zero because the discriminant is 1.
B
The equation has one zero because the discriminant is a perfect square.
C
The equation has two zeros because the discriminant is greater than 0.
D
The equation has no zeros because the discriminant is not a perfect square.
7

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.What are the solutions to the equation?

Question illustration
A
x = –1, 6
B
x = –6, 1
C
x = –22, 27
D
x = –27, 22
8

Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula?Quadratic formula: x =

Question illustration
A
StartFraction 2 plus or minus StartRoot (negative 2) squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option A
B
StartFraction negative 2 plus or minus StartRoot (negative 2) squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option B
C
StartFraction 2 plus or minus StartRoot negative 2 squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option C
D
StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option D
9

Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x = .

Question illustration
A
Zero, because the discriminant is negative.
B
Zero, because the discriminant is not a perfect square.
C
One, because the negative and the minus cancel each other out.
D
Two, because of the ± symbol.
10

What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?

A
The discriminant is equal to −16, which means the equation has no real number solutions.
B
The discriminant is equal to −16, which means the equation has two real number solutions.
C
The discriminant is equal to 24, which means the equation has no real number solutions.
D
The discriminant is equal to 24, which means the equation has two real number solutions.

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