Find the number of polynomials of the form `x^3+a x^2+b x+c` that are divisible by `x^2+1,w h e r ea , b ,c in {1,2,3,9,10}dot`

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot

If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0w h e r ea ,b ,c in Rdot

If the zeroes of the polynomial x^(3)-3x^(2)+x+1 are a-b,a,a+b find a and b.

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

Evaluate int_a^b(dx)/(sqrt(x)),w h e r ea , b > 0.

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

Show that a real value of x will satisfy the equation (1-i x)//(1+i x)=a-i b if a^2+b^2=1,w h e r ea ,b real.

Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9dot