Question

solve this question very difficult question.............
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Answer 1

GIVEN
2x^3 + ax^2 + 11x + a + 3 is divisible by 2x - 1

SOLUTION

2x - 1 = 0
2x = 1
x = 1/2

SUBSITUTE value of x in given polynomial & if it divisible by (2x - 1) then remainder must be zero.

2(1 / 2)^3 + a(1 / 2)^2 + 11(1 / 2) + a + 3 = 0
= (2 / 8) + a (1 / 4) + (11 / 2) + a + 3 = 0
= (1 / 4) + a (1 / 4) + (11 / 2) + a + 3 = 0

LCM is 4
(1 + a + 22 + 4a + 12) / 4 = 0
1 + a + 22 + 4a + 12 = 0
5a + 35 = 0
5a = - 35
a = - 35 / 5
a = - 7

Therefore, the value of must be - 7.

Answer 2

Answer:

2x - 1 = 0

2x = 1

x = 1/2

SUBSITUTE value of x in given polynomial & if it divisible by (2x - 1) then remainder must be zero.

2(1 / 2)^3 + a(1 / 2)^2 + 11(1 / 2) + a + 3 = 0

= (2 / 8) + a (1 / 4) + (11 / 2) + a + 3 = 0

= (1 / 4) + a (1 / 4) + (11 / 2) + a + 3 = 0

LCM is 4

(1 + a + 22 + 4a + 12) / 4 = 0

1 + a + 22 + 4a + 12 = 0

5a + 35 = 0

5a = - 35

a = - 35 / 5

a = - 7

Value  - 7.

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