Grade 11 · Math · Algebra 2

11th grade Quadratic equations with complex solutions worksheet

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Quadratic equations with complex solutions

Grade 11 Math Worksheet

NameDate

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

Zee's robot solves x² + 2x + 17 = 0. What is the solution with the + sign, in a + bi form?
Esme solves x² − 10x + 26 = 0 for a math club puzzle. What is the solution with the + sign, in a + bi form?
Jun solves 2x² − 4x + 10 = 0 with the quadratic formula. What is the solution with the + sign, in a + bi form?
Kira solves 4x² + 8x + 5 = 0. Use fractions if needed. What is the solution with the + sign, in a + bi form?
Luz's robot solves 9x² − 6x + 5 = 0. Use fractions. What is the solution with the + sign, in a + bi form?
Milo solves 2x² + 2x + 1 = 0. Use fractions. What is the solution with the + sign, in a + bi form?
Noah solves (x − 3)² = -25 by taking square roots. What is the solution whose i part is positive, in a + bi form?
Pia solves (x + 2)² = -9 by taking square roots. What is the solution whose i part is positive, in a + bi form?
Ren solves (x − 5)² = -49 by taking square roots. What is the solution whose i part is positive, in a + bi form?
Tala solves (x + 1)² = -36 by taking square roots. What is the solution whose i part is positive, in a + bi form?

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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