Question

for whal value of a is 2x^3 + ax^2 + 11 x + a + 3 exactly divisible by ( 2x -1 )
plz answer properly
and step by step​​

Answer 1

QUESTION :

for whal value of a is 2x^3 + ax^2 + 11 x + a + 3 exactly divisible by ( 2x -1 ).

TO FIND :

Value of a.

ANSWER :

As given polynomial p(x) is exactly divisible by (2x-1).

Then :

$2x - 1 = 0$

SO,

$2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2}$

Putting the value of x in given polynomial p(x).

$p(x) = 2 {x}^{3} + a {x}^{2} + 11x + a + 3 \\ p( \frac{1}{2} ) = 2 { \frac{1}{2} }^{3} + a( { \frac{1}{2} })^{2} + 11 \times \frac{1}{2} + \frac{1}{2} + 3$

$2 \times \frac{1}{8} + a \times \frac{1}{4} + \frac{11}{2} + a + 3 = 0\\ \frac{1}{4} + \frac{a}{4} + \frac{11}{2} + a + 3 = 0 \\ \frac{1 + a + 22 + 4a + 12}{4} = 0 \\ \frac{5a + 35}{4} = 0 \\ 5a + 35 = 0 \\ 5a = - 35 \\ a = \frac{ - 35}{5} \\ a = - 7$

FINAL ANSWER :

$a = - 5$

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Answer 2

Answer:

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