Polynomials and Rational Root Theorem

solve quadratics-easy

100

x²+2x+1=0

x=-1    x=-1

200

x²-9x-10=0

x= 10    x= -1

300

2x² +5x + 2=0

x= -1/2     x=-2

400

12x² + 17x -7 = 0

x = 1/3   x = -7/4

500

61x² - 129x -42 = 0

x = 7/3     x = -2/7

Solving Special cases

100

x² - 16 = 0 

x = 4    x = -4

200

2x² - 50 = 0

x = 5  x = -5

300

x³ + x² -4x - 4 = 0 

x= 2    x = -2    x = -1

400

7x³ +x² - 14x - 2 = 0 

x = sqrt 2      x =  -sqrt 2     x = -1/7

500

x³ - 8 = 0

x = 2    x = -1 + i sqrt 3    x = -1 - i sqrt 3

Solving using Theorem

100

x³ - 2x² - 5x + 6 = 0

x = 1    x = -2   x = 3

200

x³ - 6x² - 7x + 60 = 0

x = 5   x = -3   x = 4

300

x³ + 2x² - 11x - 12 = 0 

x = -1   x = -2  x = 2

400

5x³ + 29x² + 19x - 5

x = 1/5  x = -5   x = -1

500

2x³ + 9x² + 19x + 15

x = -3/2    x = (-3 + i sqrt 31) / 2                          x = (-3 - i sqrt 31) / 2

Mixed Review

100

x² +6x + 9 = 0

x= -3    x = -3

200

x² + 5x + 3 = 0

x = (-5 + sqrt 13) / 2       x = (-5 - sqrt 13) / 2 

300

x³ - 27 = 0

x = 3  x = (-3 + 3i sqrt 3) / 2                                  x = (-3 - 3i sqrt 3) / 2

400

x⁴ - x³ + 9x² -9x = 0 

x = 0   x = 1  x = 3i   x = -3i

500

x⁴ + 4x³ + 16 = 0 

x = -2   x = -2   x = -2   x = 2

Write Equation Standard

100

-1, 2 , 4 x³-5x²+2x+8

x³-5x²+2x+8

200

-1, -5, and 1/5

5x³ +29x²+19x-5

300

Real roots: 1, 1, and 1/4

4x³-9x³+6x-1.

400

Real roots: -1, -1, 5, 1/3

3x⁴-10x³-24x²-6x+5.

500

Real roots: 1, 1, 7, and 1/5

5x⁴-46x³+84x²-50x+7