Question

0.12. Find the value of "a" so that (2x 1) will be a factor of
2x + ax +11x+a+3​

Answer 1

Answer:

Step-by-step explanation:

If (2x+1) is a factor

Then, -1/2 should be the zero

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

       = 1/2 -1/2a-11/2+a+3=0

        = -1/2a+a+3+1/2-11/2=0

         = 1/2a +3-5=0

          = 1/2a-2 =0

          = 1/2a=2

          = a=4

Thus value of a is 4

Answer 2

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