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

How many real solutions does the equation 4x² -7x +25

No real solutions

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:  x²-14x+49

x = 7

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 -6 + 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

Factor 6x²+39x+45

What is (6x+9)(x+5)

300

Simplify the Square root of -72

What is 6i times the square root of 2

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