Question

If y3 + ay2 + by + 6 is divisible by y – 2 and leaves remainder 3 when divided by y – 3, find the values of a and

b.

Answer 1

y³ + ay² + by + 6

y = 2

8 + 4a + 2b + 6 = 0

14 + 4a + 2b = 0

7 + 2a + b = 0    .........1

If y = 3 leaves reminder 3

27 + 9a + 3b + 6 = 3  

30 + 9a + 3b =

10 + 3a + b  = 0   .........2

1 & 2

7 + 2a + b = 10 + 3a + b

a = - 3

From 1

7 + 2a + b = 0

7 - 6 + b = 0

b = - 1

Answer 2

Answer:

y³ + ay² + by + 6

y = 2

8 + 4a + 2b + 6 = 0

14 + 4a + 2b = 0

7 + 2a + b = 0    .........1

If y = 3 leaves reminder 3

27 + 9a + 3b + 6 = 3  

30 + 9a + 3b =

10 + 3a + b  = 0   .........2

1 & 2

7 + 2a + b = 10 + 3a + b

a = - 3

From 1

7 + 2a + b = 0

7 - 6 + b = 0

b = - 1