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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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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the value of 1+i^2+i^4+i^6++i^(2n)

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  2. Let x ,y ,z in R such that x+y+z=5 and x y+y z+z x=3. Thenwhat is the...

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  3. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

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  4. if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+...

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  5. Solve: i x^2-3x-2i=0,

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  6. Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a...

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  7. Express each one of the following in the standard form a+i bdot (5+...

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  8. If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum valu...

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  9. If z=4+isqrt(7) , then find the value of z^2-4z^2-9z+91.

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  10. If the quadratic equation4x^2-2(a+c-1)x+a c-b=0(a > b > c) (a...

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  11. If (a+b)-i(3a+2b)=5+2i , then find a a n d bdot

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  12. If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 h...

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  13. Given that x, y in R. Solve: x/(1+2i)+y/(3+2i)=(5+6i)/(8i-1)

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  14. If the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0...

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  15. If P(x) is a polynomial with integer coefficients such that for 4 dist...

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  16. Let x ,y ,z ,t be real numbers x^2+y^2=9, z^2+t^2=4, and xt-y z=6 Th...

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  17. If a ,b ,c are distinct positive numbers, then the nature of roots of ...

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  18. If (b^2-4a c)^2(1+4a^2)<64 a^2, a<0 , then maximum value of quadratic ...

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  19. For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo...

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  20. Find the number of integal values of x satisfying sqrt(-x^2+10x-16)...

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