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Match the following for the equation x^2...

Match the following for the equation `x^2+a|x|+1=0,w h e r ea` is a parameter. Column I, Column II No real roots, p. `a<-2` Two real roots, q. `varphi` Three real roots, r. `a=-2` Four distinct real roots, s. `ageq0`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Column I ...............................................................

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  2. If sqrt(x+i y)=+-(a+i b), then findsqrt( -x-i ydot)

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  3. Match the following for the equation x^2+a|x|+1=0,w h e r ea is a para...

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  4. Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

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  5. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

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  6. Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then...

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  7. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

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  8. Find non zero integral solutions of |1-i|^x=2^xdot

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  9. Column I, Column II If x^2+a x+b=0 has roots alpha,betaa n dx^2+p x+...

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  10. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

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  11. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

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  12. If omega is a cube root of unity, then find the value of the following...

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  13. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of ...

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  14. If omega is a cube root of unity, then find the value of the following...

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  15. Find the domain and range of f(x)=sqrt(x^2-4x+6)

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  16. Prove that |z1+z2|^2=|z1|^2+|z2|^2, ifz1//z2 is purely imaginary.

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  17. Find the range of the function f(x)=6^x+3^x+6^(-x)+e^(-x)+2.

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  18. If omega is a cube root of unity, then find the value of the following...

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  19. If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 th...

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  20. Let z1,z2, z3,......, zn be complex numbers such that |z1|=|z2|=...=|z...

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