Quiz 4.2: Complex Numbers & Quadratic Formula
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Last updated almost 4 years ago
14 questions
Note from the author:
Formulae
The imaginary number: i^{2} = -1
Discriminant: b^{2} - 4ac
Quadratic Formula: x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}
Formulae
The imaginary number: i^{2} = -1
Discriminant: b^{2} - 4ac
Quadratic Formula: x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}
1
Match the scenarios with the discriminant situation.
Match the scenarios with the discriminant situation.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
1 unique solution | arrow_right_alt | discriminant is a positive perfect square |
2 real irrational solutions | arrow_right_alt | discriminant is positive, but not a perfect square |
2 real rational solution | arrow_right_alt | discriminant is negative |
2 nonreal solutions | arrow_right_alt | discriminant is 0 |
1
Simplify the expression. Write your answer as an imaginary number, no spaces. \sqrt{-64}
Simplify the expression. Write your answer as an imaginary number, no spaces.
\sqrt{-64}
1
Simplify the expression. Write your answer as an imaginary number, no spaces.
2\sqrt{-108}
Simplify the expression. Write your answer as an imaginary number, no spaces.
2\sqrt{-108}
1
Simplify the expression. Write your answer as a number, no spaces. (-5i)(-3i)
Simplify the expression. Write your answer as a number, no spaces.
(-5i)(-3i)
1
Simplify the expression. Write your answer as a complex number, a+bi, no spaces. (8+3i)+(-6-12i)
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(8+3i)+(-6-12i)
1
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.(5-9i)-(1+4i)
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(5-9i)-(1+4i)
1
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.(9+5i)(4-2i)
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(9+5i)(4-2i)
1
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(-1-3i)^{2}
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(-1-3i)^{2}
1
Simplify the expression. Write your answer as a complex number, a+bi, no spaces. (6+i)(6-i)
Simplify the expression. Write your answer as a complex number, a+bi, no spaces.
(6+i)(6-i)
1
Solve by the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
x^{2}-10x+25=3
Solve by the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
x^{2}-10x+25=3
1
Solve using the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
x^{2}+18x+97 = 0
Solve using the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
x^{2}+18x+97 = 0
1
Solve using the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
2x^{2}+8x+134=0
Solve using the quadratic formula. Simplify all irrational and complex solutions. Use x={#, #} format, with exactly one space after the comma. List the smaller solution first.
2x^{2}+8x+134=0
1
Determine the number and type of solutions for this equation.
-2x^{2}-196 = 0
Determine the number and type of solutions for this equation.
-2x^{2}-196 = 0
1
Determine the number and type of solutions for this equation.
2x^{2}-9x+8 = 0
Determine the number and type of solutions for this equation.
2x^{2}-9x+8 = 0