Question

For what values of a is 2x ^{^{3}}+ax ^{2}+11x+a+3
exactly divisible by (2x-1) ? For what values of a is 2x ^{^{3}}+ax ^{2}+11x+a+3
exactly divisible by (2x-1) ? @Mathematics

Answer 1

\[2x ^{^{3}}+ax ^{2}+11x+a+3\]

Answer 2

you can perform division and check it... or the short cut is that if f(x) is ur expression, then put x=1/2 and f(1/2)=0 solves ur value of a...

Answer 3

-7 is ur answer...

Answer 4

Yes it matches with the answer key.
But I didn't clearly understand your previous reply. Can you explain how to do it.

Answer 5

its simple.... for the expression to be exactly divisible with the given factor,2x-1, one of the divisors of the expression can be obtained by 2x-1=0, it says x=1/2 is one of the solutions of given expression. so, by taking f(1/2), we have to get zero. thereby u can calculate the value of any unknown value in given expression.. logic is pretty simple if u understand...

Answer 6

did u get it?

Answer 7

Yes, thanks anusha_anu