Finding all Solutions of Polynomial Functions

Find all the real-number roots for the function below. Use any method you like.
f(x)=6x3−17x2+11x−2

• x = ½, ⅓, 2
• x = ¾, ½, 1
• x = ⅙, ⅚, 2
• x = 1, 2, 3

Find a polynomial function of degree 3 that has zeroes at
x=1, 2, and 3

• x³ - 6x² + 11x - 6
• x³ - 11x² - 6x - 6
• x³ - 6x² - 6x - 6
• x³ - 11x² - 11x - 11

Find all the real-number solutions for the function below. Use any method you like.
f(x)=9x4−226x2+25

• x = 5, -5, ⅓, -⅓
• x = 6, -6, ½, -½
• x = 4, -4, ¼, -¼
• x = 3, -3, ⅓, -⅓

Find all the real-number roots for the function below. Use any method you like.
f(x)=18x4+3x3−17x2+17x−55

• x = 1, -5/2, 2 +- √7 / 3
• x = 1, -3/2, 3 +- √5 / 2
• x = 1, -1/2, 4 +- √3 / 5
• x = 2, -5/2, 5 +- √7 / 4

Find a polynomial function that has zeroes at
x=4, -4, and 0

• x³ - 16x
• x³ - 8x
• x³ + 16x
• x³ + 8x

Find a polynomial function that has zeroes at
x=1+√2, 1-√2, and 1

• x³ - 3x² + x +1
• x³ - 3x² + 3x +1
• x³ - x² + x +3
• x³ - 3x² + 3x +3

Find all the real-number roots for the function below. Use any method you like.
f(x)=4x4+20x3−23x2−120x+144

• x = -4, -4, 3/2, 3/2
• x = -3, -2, -5/2, 4/2
• x = -2, -4, -3/2, -3/2
• none of the above

Find all the real-number roots for the function below. Use any method you like.
f(x)=4x3−16x2+39x−295

• x = 5, -8 +- √5 / 2
• x = 5, -7 +- √3 / 2
• x = 5, -8 +- √3 / 3
• x = 7, -8 +- √5 / 2

Find all the real-number roots for the function below. Use any method you like.
f(x)=2x3−9x2+21x−18

• x = 3/2, 3 +- √3
• x = 4/3, 3 +- √3
• x = 2/3, 3 +- √3
• x = 5/2, 3 +- √3

Find all the real-number roots for the function below. Use any method you like.
f(x)=16x3+40x2−25x−3

• x = -3, -1/10, 3/5
• x = 3, -1/10, 3/5
• x = -3, 3/10, -3/5
• x = 3, 3/10, 3/5