Question

Find the value of a and b if x - 1 and x -2 are factors of $x^{3} -ax+b$ .

Answer 1

Step-by-step explanation:

Given Equation is x³ - ax + b

(i)

(x - 1) is a factor i.e., at   x = 1 the remainder will be zero.

⇒ (1)³ - a(1) + b = 0

⇒ 1 - a + b = 0

⇒ -a + b = -1

⇒ a - b = 1

(ii)

(x - 2) is a factor i.e., at   x = 2 the remainder will be zero.

⇒ (2)³ - a(2) + b = 0

⇒ 8 - 2a + b = 0

⇒ -2a + b = -8

⇒ 2a - b = 8

On solving (i) and (ii), we get

a - b = 1

2a - b = 8

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-a = -7

a = 7

Place a = 7 in (2), we get

2a - b = -8

⇒ 2(7) - b = 8

⇒ 14 - b = 8

⇒ -b = 8 - 14

⇒ -b = -6

⇒ b = 6

Therefore,

a = 7, b = 6

Hope it helps!

Answer 2

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