Chapter 4:Solving Quadratic Equations

Radicals

100

√(32)

4√2

200

√(4x²)

2x

300

√(48n⁵)

4n²√(3n)

400

√(4/49)

2/7

500

√(a³/49)

a√(a)/7

Using Square Roots (Real solutions only!)

100

x²-16=0

x=4, x=-4

200

3x²+12=0

No real solutions

300

2x²-98=0

x=7, x=-7

400

9x²-35=14

x=7/3, x=-7/3

500

(4x+5)²=9

x=-1/2, x=-2

Quadratic Formula (Real solutions only!)

100

x²-12x+36=0

x=6

200

2x²-x-1=0

x=1, x=-1/2

300

9x²-6x+1=0

x=1/3

400

-3x²+6x=4

No real solutions

500

2x²+9x+7=3

x=-1/2, x=-4

Complex Solutions

100

√(-36)

6i

200

4x+2i=8+yi

x=2, y=2

300

9x-18i=36+6yi

x=-4, y=-3

400

(8+3i)²

55+48i

500

Find a possible pair of integer values for a and c so that the quadratic equation -4x+c=-ax² has two imaginary solutions.

ac>16

Systems

100

y=-3x²

y=6x+3

(-1,-3)

200

y=-x+7

y=-x²-2x-1

No solutions

300

y=2x²+3x-4

y-4x=2

(2,10),(-3/2,-4)

400

y=-2x²+x-3

y=2x-2

No solutions

500

y=2x-1

y=x²

(1,1)