Algebra 2--Quadratics and Complex Numbers

Quadratics 1

100

Find the discriminant and tell the types of solutions for 3x^2 + 5x - 2 = 0

What is 49, 2 real rational solutions

200

Find the discriminant and tell what type of solutions for x^2 - 3x + 4 = 0

What is -7, 2 imaginary solutions

300

One of the roots of a quadratic with real coefficients is  3 + 2i .  Find the other root.

What is 3 - 2i

400

Find all values of k, such that x^2 + kx + 27 = 0 has two real solutions for x.

plus or minus 6sqrt3

500

Find the values of a for which the equation has 2 imaginary solutions ax² + 4x - 6 = 0

 a < -2/3

Quadratics 2

100

Solve:  6x² + 13x = 8

x = 1/2, -8/3

200

Solve: x^2 - 8x + 40 = 6

What is 4+3i sqrt(2), 4-3i sqrt(2)

300

Solve: 6x² + 2 = -4x

What is -1/3 + i sqrt(2) /3 , -1/3 - i sqrt(2) / 3

400

Solve: 2x + 18/x = 15

x = 3/2, 6

500

Find the quadratic equation with real coefficients and leading term x² that has 3 + 2i as one root.

x² - 6x + 13 = 0

Complex Numbers 1

100

(2+3i) + (4+7i)

What is 6+10i

200

(2-7i) - (1-4i)

What is 1-3i

300

Simplify:  i ²⁰²¹

what is i

400

Simplify:  i ⁹⁰ 

What is -1

500

A complex number, z, plus 2 times the complex conjugate of z equals 6 - 4i.  Solve for z.

What is 2 + 4i

Complex Numbers 2

100

(3+2i)(5-i)

What is 17+7i

200

(6+2i)(6-2i)

What is 40

300

Simplify: i ¹¹ + i ¹² - i ¹³ + i ¹⁴

What is -2i

400

1/(2+3i)

What is (2-3i)/13

500

Find z such that             (2z - 3i)/(z + 4) = -5 + i

- 147/50 + (29/50)i

Misc

100

The name of the day of the year with the fewest number of daylight hours.

What is the winter solstice

200

The British word for radical (like square root or cube root).

What is "surd"

300

Find the intersection point(s) of   y = x² + 3x - 5 and y = 3x - 4

What are (-1, -7) and (1, -1)

400

Solve:  4x⁴ - 13x² + 9 = 0

x = -1, 1, -3/2, 3/2

500

Find the intersection point(s) of   y = x² + 7x - 2 and y = 4x - 5

What is no solution