Question

For what value of a is 2x³+2ax²+11+a+3 exactly divisible by (2x-1)

Answer 1

Hi ,

I think there is an error in the

question.

It may be like this ,

Let p( x ) = 2x³ + 2ax² + 11x + a + 3

It is given that ,

p( x ) divisible by ( 2x - 1 ) .

Remainder = 0

p( 1/2 ) = 0

2( 1/2 )³+2a×(1/2)²+ 11( 1/2 ) + a + 3 = 0

2/8 + 2a/4 + 11/2 + a + 3 = 0

1/4 + a/2 + a + 11/2 + 3 = 0

( 1 + 2a + 4a + 22 + 12 )/4 = 0

6a + 35 = 0

6a = -35

a = -35/6

I hope this helps you.

: )

Answer 2

Hiii friend,

P(X) = 2X³+2AX²+11X+A+3

(2X-1) = 0

2X = 1


X = 1/2.

Putting X = 1/2

P(1/2) = 2 × (1/2)³ + 2 × A × (1/2)² + 11 × 1/2 + A +3

=> 2 ×1/8 + 2 × A × 1/4 + 11/2 + A +3

=> 1/4 +2A/4 + 11/2 + A +3

=> 1/4 + A/2 + 11/2 + A + 3


=> 1 + 2A + 22 + 4A +12

=> 6A + 35 = 0

=> 6A = -35

=> A = -35/6



HOPE IT WILL HELP YOU...... :-)