Question

Q7. If the polynomials 3x^3+ ax^ 2 + 3x + 5 and 4x^3+x²-2x+a leave the same remainder when divided by (x-2), find the value of a. Also find the remainder in each case.​

Answer 1

Answer:

a=-1

1. x-2»x=2
2. p(x)=3x³+ax²+ 3x+5
3. p(2)=3(2)³+a(2)²+3(2)+5
4. p(2)=3(8)+a(4)+6+5
5. p(2)=24+4a+11
6. p(2)=4a+35--------------(eq.-1)

1. p(x)=4x³+x²-2x+a
2. p(2)=4(2)³+(2)²-2(2)+a
3. p(2)=4(8)+4-4+a
4. p(2)=a+32--------------------(eq.-2)

equate 1 and 2

a+32=4a+35

a-4a=35-32

-3a=3

a=3/-3

a=-1

Answer 2

Answer:

Step-by-step explanation:

According to remainder theorem, for a to be the remainder, x = 2.

For the first equation, 24 + 4a + 6 + 5

For the second one - 32 + 4 -4 + a

=> 35 + 4a = 32 + a

=> a = -1