Show that the polynomial x^(4p)+x^(4q+1)...

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`

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Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^(3)+x^(2)+x+1, where p,q,r,s in n

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Let polynomial P(x)=x^(5)+2x^(4)-x^(3)+2x^(2)+3 ,is divided by polynomial D(x)=x^(2)-x+2 then we get remainder "R(x)" and quotient "Q(x)" such that P(x)=Q(x)*D(x)+R(x) then : (A) Q(x)=x^(3)+3x^(2)-4x, (B) Q(x)=x^(3)+3x^(2)-4 (C) R(x)=-4x+11, (D) R(x)=4x+11

The HCF of the polynomials 9(x +a)^(p) (x -b)^(q) (x + c)^(r) and 12(x + a)^(p +3) (x -b)^(q-3) (x +c)^(r +2) " is " 3(x +a)^(6) (x -b)^(6) (x + c)^(6) , then the value of p +q -r is

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...
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If omega is a cube root of unity but not equal to 1, then minimum valu...
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If one of the vertices of the square circumscribing the circle |z - 1|...
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If z1 and z2, are two non-zero complex numbers such tha |z1+z2|=|z1...
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If 1,omega,omega^(2) are the cube roots of unity, then the roots of t...
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If omega = z//[z-(1//3)i] and |omega| = 1, then find the locus of z.
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If w=alpha+ibeta where Beta 0 and z ne 1 satisfies the condition that...
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Find the value of sum(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wher...
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If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...
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A man walks a distance of 3 units from the origin towards north-east t...
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If |z|=1 and z!=+-1, then all the values of z/(1-z^2) lie on
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If abs(z+4) le 3, the maximum value of abs(z+1) is
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Let A, B, C be three sets of complex number as defined below: A={z:Img...
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Let A,B and C be three sets of complex numbers as defined below: {:(,A...
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Let A,B and C be three sets of complex numbers as defined below: {:(,A...
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A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...
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If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...
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Let z=x+i y be a complex number where xa n dy are integers. Then, the ...
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Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1...
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If |Z-4/Z|=2 then maximum value of |Z| is equal to
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Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...
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