## Complex Number and Quadratic Equations Quiz-14

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 a,b,c,d∈R, then the equation (x2+ax-3b)(x2-cx+b)(x2-dx+2b)=0 has
•  6 real roots
•  At least 2 real roots
•  4 real roots
•  3 real roots
Solution
Q2. If a,b,c be distinct positive numbers, then the nature of roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=1/x is
•  All real and distinct
•  All real and at least two are distinct
•  At least two real
•  All non-real
Solution

Q3. If the roots of the quadratic equation (4p-p2-5) x2-(2p-1)x+3p=0 lie on either side of unity, then the number of integral values of p is
•  1
•  2
•  3
•  4
Solution

Q4. If k>0,|z|=|w|=k and Î±=(z-w ̅)/(k2+zw ̅ ), then Re(Î±) equals
•  0
•  k/2
•  k
•  None of these
Solution
(a)

Q5. Let f(x)=(1+b2 ) x2+2bx+1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is
•  [0,1]
•  (0,1/2]
•  [1/2,1]
•  (0,1]
Solution

Q6. The coefficient of x in the equation x2+px+q=0 was wrongly written as 17 in place of 13 and the roots thus found was -2 and -15. Then the roots of the correct equation are
•  -3,10
•  -3,-10
• 3,-10
•  None of these
Solution

Q7. If 8iz3+12z2-18z+27i=0, then
•  |z|=3/2
•  |z|=2/3
•  |z|=1
•  |z|=3/4
Solution

Q8. If ‘z’ lies on the circle |z-2i|=2√2 then the value of arg⁡〖[(z-2)/(z+2)]〗 is equal to
•  Ï€/3
•  Ï€/4
•  Ï€/6
•  Ï€/2
Solution

Q9.  If ‘p’ and ‘q’ are distinct prime numbers, then the number of distinct imaginary numbers which are pth as well as qth roots of unity are
•  min⁡(p,q)
•  max⁡(p,q)
•  1
•  Zero
Solution

Q10. Let a be a complex number such that |a|<1 and z1,z2,z3,… be the vertices of a polygon such that zk=1+a+a2+⋯+a(k-1) for all k=1,2,3,… then z1,z2,…. lie within the circle
•  |z-1/(1-a)|=1/|a-1|
•  |z+1/(a+1)|=1/(|a+1|)
•  |z-1/(1-a)|=|a-1|
• |z+1/(a+1)|=|a+1|
Solution

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