Question

Find the values of a and b if x -1 and x - 2 are factors of x^3- ax + b

Answer 1

Given,

equation,

x³ - ax + b

given zeros = x - 1 and x - 2

at,

x = 1

1 - a + b = 0

a - b = 1 ...(1)

at x = 2

8 - 8a + b = 0

8a - b = 8 ....(2)

(1) - (2)

7a = 7

a = 1

from (1),

a - b = 1

1 - b = 1

b = 0

a = 1

Answer 2

Given,

equation,

x³ - ax + b

given zeros = x - 1 and x - 2

at,

x = 1

1 - a + b = 0

a - b = 1 ...(1)

at x = 2

8 - 8a + b = 0

8a - b = 8 ....(2)

(1) - (2)

7a = 7

a = 1

from (1),

a - b = 1

1 - b = 1

b = 0

a = 1