Quadratic Equations with Complex Solutions: Algebra 2 Math Quiz – PDF Download
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
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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.
AOne real solution
BNo real solutions
CTwo real solutions
DInfinitely 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\(x=\pm 3i\)
DNo solutions at all
Question 4
The equation \(x^{2}-10x+25=0\) has which kind of solutions?
ATwo different real solutions
BOne repeated real solution
CTwo complex solutions
DNo 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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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.
