Question

Given that (x + 2) and (x - 1) are the factors of x.x.x + a.x.x + b.x - 6. Find a and b.

Please answer correctly and asap. I'll mark u as brainliest please.​

Answer 1

Answer:

a = 4, b = 1

Step by step explanation:

f ( x ) = x^3 + a.x^2 + b.x - 6

x + 2 = 0 => x = -2

x - 1 = 0 => x = 1

f ( -2 ) = (-2)^3 + a.(-2)^2 + b.(-2) - 6

0 = -8 + 4a - 2b - 6

0 = -14 + 4a - 2b

4a - 2b = 14

2a - b = 7 - ( i )

f ( 1 ) = 1^3 + a. 1^2 + b. 1 - 6

0 = 1 + a + b - 6

0 = -5 + a + b

a + b = 5 - ( ii )

Adding ( i ) and ( ii )

2a - b = 7

a + b = 5

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3a = 12

a = 12/3

a = 4

Putting a = 4 in ( ii )

a + b = 5

4 + b = 5

b = 5 - 4

b = 1