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Find the values of `a` for which the roots of the equation `x^2+a^2=8x+6a` are real.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve the equation |z|=z+1+2idot

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  2. If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

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  3. Find the values of a for which the roots of the equation x^2+a^2=8x+6...

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  4. If alpha and beta are different complex numbers with |beta|=1, then...

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  5. If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. 1 d. 2

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  6. 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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  7. 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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  8. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

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

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

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

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

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

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

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

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

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

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

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

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