Solving Quadratic Equations with Real and Imaginary Solutions

Authored by Linda Miragliotta

Mathematics

12th Grade

CCSS covered

Used 3+ times

Solving Quadratic Equations with Real and Imaginary Solutions

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25 questions

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REORDER QUESTION

15 mins • 4 pts

Reorder the following steps for solving quadratics by square roots.

Take the SQUARE ROOT of both sides

REWRITE the equation as x² = n

SIMPLIFY the radical. Place "±" to indicate both answers.

If there is a NEGATIVE SQUARE ROOT, rewrite $\sqrt[]{-a}$ as $\sqrt[]{-1\cdot a}$ and break $a$ down if it is not a perfect square.

SIMPLIFY the radical, recalling that $\sqrt[]{-1}=i$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
x² − 64 = 0

x = ±8

x = ±64

x = ±32

x = ±16

x = ±4

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
7x² + 8 = 15

x = ±1

x = ±2

x = ±3

x = ±4

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
81x² + 5 = 21
What is the value of x?

x = 2

x = -2

x = 1

x = -1

x = $\pm\frac{4}{9}$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
8x² + 1 = 17

x = ±2

x = ±1

x = ±3

x = ±4

$x=\pm\sqrt[]{2}$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
2x² − 9 = 55

x = ±4

x = ±5

x = ±6

x = ±7

$x=\pm4\sqrt[]{2}$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
9x² + 3 = 111

x = ±4

x = ±3

$x=\pm3\sqrt[]{2}$

x = ±2

$x=\pm2\sqrt[]{3}$

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method
4 − 3x² = -77

x = ±5

x = ±3

x = ±4

x = ±6

$x=\pm3\sqrt[]{3}$

Tags

CCSS.8.EE.A.2

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
5x² + 10 = 310

$x=\pm5\sqrt[]{2}$

x = ±6

x = ±7

x = ±5

$x=\pm2\sqrt[]{15}$

Tags

CCSS.HSA-REI.B.4B

10.

MULTIPLE CHOICE QUESTION

15 mins • 4 pts

Solve the equation using the square roots method:
$-\frac{1}{2}x^2+1=-39$

x = ±8

x = ±20

$x=\pm4\sqrt[]{5}$

No Real Solution

$x=\pm5\sqrt[]{4}$

Tags

CCSS.HSA-REI.B.4B

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Solving Quadratic Equations with Real and Imaginary Solutions

Reorder the following steps for solving quadratics by square roots.

Solve the equation using the square roots method: x2 − 64 = 0

Solve the equation using the square roots method: 7x2 + 8 = 15

Solve the equation using the square roots method: 81x2 + 5 = 21What is the value of x?

Solve the equation using the square roots method: 8x2 + 1 = 17

Solve the equation using the square roots method: 2x2 − 9 = 55

Solve the equation using the square roots method: 9x2 + 3 = 111

Solve the equation using the square roots method4 − 3x2 = -77

Solve the equation using the square roots method: 5x2 + 10 = 310

Solve the equation using the square roots method: −12x2+1=−39-\frac{1}{2}x^2+1=-39−21​x2+1=−39

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Solve the equation using the square roots method:
x² − 64 = 0

Solve the equation using the square roots method:
7x² + 8 = 15

Solve the equation using the square roots method:
81x² + 5 = 21
What is the value of x?

Solve the equation using the square roots method:
8x² + 1 = 17

Solve the equation using the square roots method:
2x² − 9 = 55

Solve the equation using the square roots method:
9x² + 3 = 111

Solve the equation using the square roots method
4 − 3x² = -77

Solve the equation using the square roots method:
5x² + 10 = 310

Solve the equation using the square roots method:
$-\frac{1}{2}x^2+1=-39$