Question

For what value a is 2x^3+ax^2+11x+a+3 exactly divisible by (2x-1)

Answer 1

Answer:

2x - 1 must be a factor of the given polynomial.

One of the roots must be x = 1/2

Now, x = 1/2, and equate the polynomial to zero:

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

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

5a/4 + 35/4 = 0

5a + 35 = 0

a = -7

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