Complex Number and Quadratic Equations Quiz-17

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.  z1 and z2 are two distinct points in an Argand plane. If a|z1 |=b|z2 | (where a,b∈R), then the point (az1/bz2)+(bz2/az1) is a point on the
•  Line segment [-2,2] of the real axis
•  Line segment [-2,2] of the imaginary axis
•  Unit circle |z|=1
•  The line with arg⁡〖z= tan(-1)⁡2 〗
Solution
Q2. The number of complex numbers z satifying |z-3-i|=|z-9-i| and |z-3+3i|=3 are
•  One
•  Two
•  Four
•  None of these
Solution

Q3. If ‘z’ is complex number then the locus of ‘z’ satisfying the condition |2z-1|=|z-1| is
•  Perpendicular bisector of line segment joining 1/2 and 1
•  Circle
•  Parabola
•  None of the above curves
Solution

Q4. If xy=2(x+y),x≤y and x,y∈N, then the number of solutions of the equation are
•  Two
•  Three
•  No solution
•  Infinitely many solutions
Solution

Q5. If the roots of the equation x2-2ax+a2+a-3=0 are real and less than 3, then
•  a<2
•  2≤a≤3
•  3<a≤4
•  a>4
Solution

Q6. Let f(x)=ax2+bx+c,a,b,c∈R. If f(x) takes real values for real values of x and non-real values of x, then
•  a=0
•  b=0
• c=0
•  Nothing can be said about a,b,c
Solution

Q7. If z(1+a)=b+ic and a2+b2+c2=1, then[(1+iz)/(1-iz)=
•  (a+ib)/(1+c)
•  (b-ic)/(1+a)
•  (a+ic)/(1+b)
•  None of these
Solution

Q8. The number of positive integral solutions of x4-y4=3789108 is
•  0
•  1
•  2
•  4
Solution

Q9.  Let a,b and c be real numbers such that 4a+2b+c=0 and ab>0. Then the equation ax2+bx+c=0 has
•  Complex roots
•  Exactly one root
•  Real roots
•  None of these
Solution
(c)
Clearly, x=2 is a root of the equation and imaginary roots always occur in pairs. Therefore, the other root is also real
Q10. If Ï‰(≠1) is a cube root of unity and (1+Ï‰)7=A+BÏ‰ then A and B are respectively
•  0, 1
•  1, 1
•  1,0
• -1,1
Solution

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