Find the value of 'a' for which 2x3+ax2+11x+a+3 is exactly divisible by 2x-1
Please show the whole solution also because I tried many times to do it but I can't able to do so please show the whole solution
Answers
Answered by
657
Dear Student,
Answer: a = -7
Solution:
from polynomial 2x-1
put the value of x,in cubic polynomial,and solve for a.

if given polynomial is exactly divisible by 2x-1, than on putting x = 1/2, it becomes zero.

The value of a = -7.
Hope it helps you.
Answer: a = -7
Solution:
from polynomial 2x-1
put the value of x,in cubic polynomial,and solve for a.
if given polynomial is exactly divisible by 2x-1, than on putting x = 1/2, it becomes zero.
The value of a = -7.
Hope it helps you.
Answered by
231
GIVEN : Let Polynomial f(x)=2x³+ax²+11x+a+3 …….(1)
Polynomial is exactly divisible by 2x-1 if the remainder is 0.
2x -1= 0
2x = 1
x = ½
By remainder theorem, when f(x) is divided by (2x-1) then remainder = f(½)
On Putting x= ½ in eq 1
f(1/2)=2(1/2)³+a(1/2)²+11(1/2)+a+3
0 =2(⅛)+a/4+11/2+a+3
0 = ¼+a/4+11/2+a+3
0 = ¼ + 11/2 +3 +a/4 +a
0 = (1+22+12)/4 +(a + 4a)/4
0= 35/4 + 5a/4
-35/4 = 5a/4
-35 = 5a
a = -35/5
a = -7
Hence, the value of a is -7
HOPE THIS ANSWER WILL HELP YOU…
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