## Complex Number and Quadratic Equations Quiz-20

Complex numbers and quadratic equations is a segment of maths that deals with crucial theorems and concepts along with various formulae. It comprises of linear and quadratic equations along with roots related to the complex number's set (known as complex roots)..

Q1.  1,z1,z2,z3,…,z(n-1) are the nth roots of unity, then the value of 1/(3-z1)+1/(3-z2)+⋯+1/(3-z(n-1)) is equal to
•  (n3(n-1))/(3n-1)+1/2
•  (n3(n-1))/(3n-1)-1
•  (n3(n-1))/(3n-1)+1
•  None of these
Solution
Q2. Given z=〖(1+i√3)〗100, then [RE(z)/IM(z)] equals
•  2100
•  250
•  1/√3
•  √3
Solution

Q3. The quadratic x2+ax+b+1=0 has roots which are positive integers, then (a2+b2) can be equal to
•  50
•  37
•  61
•  19
Solution

Q4. x1 and x2 are the roots of ax2+bx+c=0 and x1 x2<0. Roots of x1 (x-x2 )2+x2 (x-x1 )2=0 are
•  Real and opposite sign
•  Negative
•  Positive
•  Non-real
Solution

Q5. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always
•  Positive
•  Real
•  Negative
•  None of these
Solution

Q6. If a2+b2+c2=1, then ab+bc+ca lies in the interval
•  [1/2,2]
•  [-1,2]
• [-1/2,1]
•  [-1,1/2]
Solution

Q7. If |z1 |= |z2 | and arg arg⁡〖(z1/z2)=Ï€〗, then z1+z2is equal to
•  0
•  Purely imaginary
•  Purely real
•  None of these
Solution

Q8. If b1 b2=2(c1+c2), then at least one of the equations x2+b1 x+c1=0 and x2+b2 x+c2=0 has
•  Imaginary roots
•  Real roots
•  Purely imaginary roots
•  None of these
Solution

Q9.  If cos⁡Î±+2cos⁡Î²+3cos⁡Î³=sin⁡Î±+2sin⁡Î²+3sin⁡Î³=0, then the value of sin⁡3Î±+8sin⁡3Î²+27sin⁡3Î³ is
•  sin⁡(a+b+Î³)
•  3sin⁡(Î±+Î²+Î³)
•  18sin⁡(Î±+Î²+Î³)
•  sin⁡(Î±+2Î²+3)
Solution
Q10. If z=x+iy and Ï‰=(1-iz)/(z-i), then |Ï‰|=1 implies that, in the complex plane
•  z lies on the imaginary axis
•  z lies on the real axis
•  z lies on the unit circle
• None of these
Solution

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