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If the equation z^4+a1z^3+a2z^2+a3z+a4=0...

If the equation `z^4+a_1z^3+a_2z^2+a_3z+a_4=0` where `a_1,a_2,a_3,a_4` are real coefficients different from zero has a pure imaginary root then the expression `(a_3)/(a_1a_2)+(a_1a_4)/(a_2a_3)` has the value equal to

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of...

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  2. If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is pure...

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  3. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

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  4. If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder whe...

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  5. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

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  6. Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, t...

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  7. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

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  8. If z1, z2, z3 be the affixes of the vertices A, B and C of a triangle...

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  9. The number of complex numbers z such that |z|=1 and |z/ barz + barz/z...

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  10. Given that x^2-3x+1=0, then the value of the expression y=x^9+x^7+x^(-...

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  11. If i z^4+1=0, then prove that z can take the value cospi//8+isinpi//...

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  12. Find the value of x such that ((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(s...

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  13. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

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  14. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

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  15. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

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  16. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

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  17. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

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  18. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

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  19. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then the value x^3+...

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  20. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

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