## Complex Number and Quadratic Equations Quiz-16

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. If z1 is a root of the equation a0 zn+a1 z(n-1)+⋯+a(n-1) z+an=3, where |ai |< 2 for i=0,1,…,n. Then
•  |z1 |>1/3
•  |z1 |<1/4
•  |z1 |>1/4
•  |z|<1/3
Solution
Q2. The complex numbers z1,z2 and z3 satisfying [(z1-z3)/(z2-z3)]=[(1-i√3)/2] are the vertices of a triangle which is
•  Of area zero
•  Right-angled isosceles
•  Equilateral
•  Obtuse-angled isosceles
Solution

Q3. The number of solutions of the equation z2+z ̅ =0 is
•  1
•  2
•  3
•  4
Solution

Q4. If Î± is the nth root of unity, then 1+2Î±+3Î±2+⋯ to n terms equal to
•  (-n)/(1-Î±)2
•  (-n)/(1-Î±)
•  (-2n)/(1-Î±)
•  (-2n)/(1-Î±)2
Solution

Q5. If Î±,Î² be the roots of the equation 2x2-35x+2=0, then the value of (2Î±-35)3 (2Î²-35)3 is equal to
•  8
•  1
•  64
•  None of these
Solution

Q6. If z is a complex number such that –Ï€/2≤arg⁡z≤Ï€/2, then which of the following inequality is true?
•  |z-¯z|≤|z|(arg⁡〖z-arg⁡¯z 〗)
•  |z-¯z|≥|z|(arg⁡〖z-arg⁡¯z 〗)
• |z-¯z|<(arg⁡〖z-arg⁡¯z 〗)
•  None of these
Solution

Q7. If x2+ax-3x-(a+2)=0 has real and distinct roots, then minimum value of (a2+1)/(a2+2) is
•  1
•  0
•  1/2
•  1/4
Solution

Q8. If Î± and Î² are the roots of the equation x2-ax+b=0 and An=Î±n+Î²n, then which of the following is true?
•  A(n+1)=aAn+bA(n-1)
•  A(n+1)=bAn+aA(n-1)
•  A(n+1)=aAn-bA(n-1)
•  A(n+1)=bAn-aA(n-1)
Solution

Q9.  The polynomial x6+4x5+3x4+2x3+x+1 is divisible by where w is cube root of units Where Ï‰ is one of the imaginary cube roots of unity
•  x+Ï‰
•  x+Ï‰2
•  (x+Ï‰)(x+Ï‰2)
•  (x-Ï‰)(x-Ï‰2)
Solution

Q10. Let f(x)=ax2+bx+c,a≠0 and ∆=b2-4ac. If Î±+Î²,Î±2+Î²2 and Î±3+Î²3 are in GP, then
•  ∆≠0
•  b∆=0
•  c∆=0
• bc≠0
Solution

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