Home
Class 12
MATHS
The number of polynomials of the form x^...

The number of polynomials of the form `x^(3)+ax^(2)+bx+c` that are divisible by `x^(2)+1`, where a, b,c`in{1,2,3,4,5,6,7,8,9,10}`, is

A

10

B

15

C

5

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
We have `i^(3)+ai^(2)+bi+c=0`
and `(-i)^(3)+a(-i)^(2)+b(-i)+c=0`
`implies(c-a)+(b-1)i=0`
and `(c-a)-i(b-1)+0`
`impliesb=1,a=c`
thus, total number of such polynomials`=.^(10)C_(1)=10`
Promotional Banner

Similar Questions

Explore conceptually related problems

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c , then a, b, c, d are in

If the polynomial 7x^(3)+ax+b is divisible by x^(2)-x+1 , find the value of 2a+b.

Find the value of a for which the polynomial 3x^(3)+14x^(2)+9x+a is divisible by 3x+5 .

A={1,2,3,4,5,6,7,8,9,10}, B={2,3,5,7}. Find A cap B

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8} , which of the following may be considered as universal set (s) for all the three sets A, B and {0,1,2,3,4,5,6,7,8,9,10}

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8} , which of the following may be considered as universal set (s) for all the three sets A, B and C {1,2,3,4,5,6,7,8}

The equation formed by decreasing each root of ax^(2)+bx+c=0 by 1 is 2x^(2)+8x+2=0 then

Find the matrix X so that , X[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4,6):}] .

If x-1 is a factor of 2x^(3)+ax^(2)+2bx+1 and 2a-b=4 . Find the values of a and b.