Algebra 2 Quadratics Complex Solutions Quiz

Contents

This algebra 2 quadratics complex solutions quiz asks 10 multiple-choice questions on quadratic equations with complex solutions, and each answer comes with a short explanation.

Ten multiple-choice questions on quadratic equations with complex solutions: the discriminant, graphs that miss the x-axis, the quadratic formula with i and conjugate pairs. Choose one answer for each, then read the explanation to find the typical mistake.

Algebra 2Common Core: N-CN.C.7 · A-REI.B.4b

🎯 Quadratic Equations with Complex Solutions – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

The graph of \(y=x^{2}-2x+4\) is shown. How many real solutions does \(x^{2}-2x+4=0\) have?

A parabola.

A One real solution

B No real solutions

C Two real solutions

D Infinitely many

Question 2

What is the discriminant of \(x^{2}+3x+5=0\)?

A \(-11\)

B \(29\)

C \(11\)

D \(1\)

Question 3

What are the solutions of \(x^{2}+9=0\)?

A \(x=\pm 3\)

B \(x=3i\)

C \(x=\pm 3i\)

D No solutions at all

Question 4

The equation \(x^{2}-10x+25=0\) has which kind of solutions?

A Two different real solutions

B One repeated real solution

C Two complex solutions

D No solutions

Question 5

What are the solutions of \(x^{2}-2x+5=0\)?

A \(x=1\pm 4i\)

B \(x=2\pm 2i\)

C \(x=-1\pm 2i\)

D \(x=1\pm 2i\)

Question 6

The two solutions of a quadratic equation with real coefficients are plotted. Which equation has them as solutions?

Two points in the complex plane.

A \(x^{2}-6x+13=0\)

B \(x^{2}+6x+13=0\)

C \(x^{2}-6x+5=0\)

D \(x^{2}-6x-13=0\)

Question 7

What is the sum of the solutions of \(x^{2}-4x+20=0\)?

A \(4\)

B \(-4\)

C \(20\)

D \(2\)

Question 8

One solution of a quadratic with real coefficients is \(5+2i\). What is the other solution?

A \(-5-2i\)

B \(-5+2i\)

C \(2+5i\)

D \(5-2i\)

Question 9

For which value of \(k\) does \(x^{2}+4x+k=0\) have two complex solutions?

A \(k=4\)

B \(k=3\)

C \(k=7\)

D \(k=0\)

Question 10

The graph of \(y=ax^{2}+bx+c\) touches the x-axis at exactly one point. What is true?

A parabola touching the x-axis.

A \(b^{2}-4ac>0\)

B \(b^{2}-4ac< 0\)

C \(b^{2}-4ac=1\)

D \(b^{2}-4ac=0\)

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

The discriminant is D = b² − 4ac.
D > 0: two real solutions; D = 0: one repeated real solution; D < 0: two complex solutions.
For D < 0, √D = i√(−D), so the solutions have the form p ± qi.
Complex solutions of a real quadratic always come as a conjugate pair.
Square roots, completing the square, and the formula all reach the same solutions.