Grade 11 · Math · Algebra 2

11th grade Quadratic equations with complex solutions worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Quadratic equations with complex solutions

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Noah checks x² + 4x + 20 = 0 for a math club puzzle. Here a = 1, b = 4 and c = 20. What is b² − 4ac?
Pia starts the quadratic formula for x² − 6x + 10 = 0, with a = 1, b = -6 and c = 10. What is b² − 4ac?
Ren's robot reads 2x² − 4x + 5 = 0: a = 2, b = -4, c = 5. What is b² − 4ac?
Tala works on x² + 2x + 26 = 0, where a = 1, b = 2 and c = 26. What is b² − 4ac?
5.
Zee solves x² + 36 = 0 on a puzzle card. Which shows all the solutions?
- x = 6i
- x = 6i or x = -6i
- x = 6 or x = -6, with the i dropped
- No solution
6.
Esme writes x² = -64 on the board. Which shows all the solutions?
- No solution
- x = 8 or x = -8, with the i left off
- x = 8i or x = -8i
- x = 8i
7.
Kira solves x² + 121 = 0 for a math club puzzle. Which shows all the solutions?
- x = 11 or x = -11
- x = 11i
- No solution
- x = 11i or x = -11i
Luz uses the formula on x² + 2x + 10 = 0. Here b² − 4ac = 4 − 40 = -36. What is √(-36), written with i?
Milo solves x² − 4x + 8 = 0. Here b² − 4ac = 16 − 32 = -16. What is √(-16), written with i?
Pia finds b² − 4ac = 4 − 200 = -196 for x² − 2x + 50 = 0. What is √(-196), written with i?

Quadratic equations with complex solutions. Every version has 10 questions, and the answer key prints on the second page.

I can find b² − 4ac and say that a negative value gives two solutions with i.
I can solve a quadratic with the formula or square roots and write the solutions as a ± bi.
I can check a solution by substituting it, and build a quadratic from its two solutions.

Standard: N-CN.C.7, A-REI.B.4

discriminant: b² − 4ac, the number under the root in the formula.

mirror pair: a + bi and a − bi: one above the real axis, one below.

± (plus or minus): Do it twice: once with +, once with −.

substitute: Put a number in for x and work it out.

Your child added 4ac instead of subtracting it.

Your child doubled b instead of squaring it.

Your child made b² negative when b was negative.

Ask: in b² − 4ac, is 4ac added or taken away?

Ask: is b² the same as 2 × b?

Ask: what is (-6) × (-6)?

What is the most common mistake with quadratic equations with complex solutions?

Your child added 4ac instead of subtracting it.

How can I help my child with quadratic equations with complex solutions?

Ask: in b² − 4ac, is 4ac added or taken away?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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