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Unit 5 Solving Quadratic Equations w./ Imaginary Roots - Printable Mathematics Worksheets - Wayground

Unit 5 Solving Quadratic Equations w./ Imaginary Roots

10 questions

10th - 10th Grade

Mathematics

Unit 5 Solving Quadratic Equations w./ Imaginary Roots is a Grade 10 mathematics worksheet with 10 multiple-choice questions. It focuses on solving quadratic equations that produce nonreal solutions, identifying functions with imaginary zeros, and writing solutions with the imaginary unit i. Several items require students to use square roots to solve equations such as x² = -100 and (x − 1)² + 3 = −1, while others ask students to recognize solution sets and simplify imaginary radical answers. This free printable worksheet helps students connect negative quantities under square roots with pairs of complex solutions, including ± notation and expressions such as -2i√10 and 2i√10. It is useful for guided practice, independent work, or a quick check of understanding after instruction on imaginary roots. The worksheet includes a complete answer key so teachers can review students’ reasoning and identify errors in sign, square-root, or solution-set notation.

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Worksheets

Unit 5 Solving Quadratic Equations w./ Imaginary Roots

Total questions: 10

Name
Class
Date
1.

Solve 7x2+21=07x^2+21=0  

a)

x=−3x=-3  

b)

3i3i  

c)

x=±3x=\pm\sqrt{3}  

d)

x=±i3x=\pm i\sqrt{3}  

2.

Which function(s) has imaginary zeros?

a)

h

b)

f, g

c)

f

d)

h, g

3.

What is the solution set for the equation x2 + 64 = 0

a)

{-8, 8}

b)

{-8i, 8i}

c)

{-16i, 16i}

d)

{-64i, 64i}

4.

Solve: 4x2+15 = −94x^2+15\ =\ -9  

a)

x = ±2i3x\ =\ \pm2i\sqrt{3}  

b)

x = ±6ix\ =\ \pm6i  

c)

x = ±i6x\ =\ \pm i\sqrt{6}  

d)

x = ±3i2x\ =\ \pm3i\sqrt{2}  

5.

Solve.   x² = -100

a)

x = 10i

b)

x = ± 10i

c)

x = ±10

d)

x = √10

6.

Solve the following using square roots:

 (x−1)2+3=−1\left(x-1\right)^2+3=-1

a)

 x=1±4ix=1\pm4i

b)

 x=1±2ix=1\pm2i

c)

 x=1±3ix=1\pm3i

d)

 x=1±5ix=1\pm5i

7.

Solve the following using square roots:

x2+36=0x^2+36=0

a)

x=±6ix=\pm6i

b)

x=±6x=\pm6

c)

x=±36x=\pm36

d)

x=±62x=\pm6\sqrt{2}

8.

Solve the following equation using square roots:

−2(x+4)2=25-2\left(x+4\right)^2=25

a)

x=−4±5i22x=-4\pm\frac{5i\sqrt[]{2}}{2}

b)

x=−4±522x=-4\pm\frac{5\sqrt[]{2}}{2}

c)

x=−4±5i2x=-4\pm\frac{5i}{2}

d)

x=−4±52x=-4\pm\frac{5}{2}

9.
x2+141=20
a)
-11i, 11i 
b)
-11i
c)
11i
d)
no solution
10.
-5x2=200
a)
-10i√2,10i√2
b)
2i√10
c)
-2i√10
d)
-2i√10,2i√10
Answer Key

Unit 5 Solving Quadratic Equations w./ Imaginary Roots

Total questions: 10

1.
d)

x=±i3x=\pm i\sqrt{3}  

2.
a)

h

3.
b)

{-8i, 8i}

4.
c)

x = ±i6x\ =\ \pm i\sqrt{6}  

5.
b)

x = ± 10i

6.
b)

 x=1±2ix=1\pm2i

7.
a)

x=±6ix=\pm6i

8.
a)

x=−4±5i22x=-4\pm\frac{5i\sqrt[]{2}}{2}

9.
a) -11i, 11i 
10.
d) -2i√10,2i√10

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FAQs

What does this worksheet cover?

This Grade 10 worksheet covers solving quadratic equations with imaginary roots, especially equations that can be rearranged and solved using square roots. Its 10 multiple-choice items ask students to identify imaginary zeros, write solutions such as ±10i, solve shifted equations such as (x − 1)² + 3 = −1, and express simplified imaginary radical solutions.

How can I use this worksheet to teach solving quadratic equations with imaginary roots?

Introduce the worksheet by modeling how to isolate the squared expression, take the square root of a negative number, and write both ± solutions. Then have students explain why equations such as x² + 64 = 0 produce {-8i, 8i}, and use the multiple-choice options to discuss the difference between real roots, imaginary roots, and no solution. Finish with the square-root items as guided-to-independent practice.

What mistakes should I watch for when students complete this worksheet?

Watch for students replacing √−a with a real number, omitting the ± when solving a squared equation, or giving only one member of a solution set. Students may also lose the horizontal shift in equations such as (x − 1)² + 3 = −1 or simplify imaginary radicals incorrectly, as in the item whose solutions are -2i√10 and 2i√10.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 10 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital version can be assigned through Wayground for online completion and scoring.

How can I differentiate this imaginary-roots worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the quadratic expressions, ± symbols, and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping its multiple-choice format.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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