19. For what value of p is 2x3 + px2 + 11x + p + 3 exactly divisible b

1.	19. For what value of p is 2x3 + px2 + 11x + p + 3 exactly divisible by (2x – 1) ?
Answer» <P>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 HOPE THIS ANSWER WILL HELP YOU…

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

Answer»

<P>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

HOPE THIS ANSWER WILL HELP YOU…

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

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

HOPE THIS ANSWER WILL HELP YOU…

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