Quiz 4.2: Complex Numbers & Quadratic Formula

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.

Draggable itemCorresponding Item
1 unique solution
discriminant is a positive perfect square
2 real irrational solutions
discriminant is positive, but not a perfect square
2 real rational solution
discriminant is negative
2 nonreal solutions
discriminant is 0
1

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}

1

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)

1

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)

1

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)

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

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

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

1

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