Question

19. For what value of p is 2x3 + px2 + 11x + p + 3 exactly divisible by (2x – 1) ?​

Answer 1

Answer:

Replace p with a

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

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