## Complex Number and Quadratic Equations Quiz-19

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 z is a complex number having least absolute value and |z-2+2i|=1, then z=
•  (2-1/√2)(1-i)
•  (2-1/√2)(1+i)
•  (2+1/√2)(1-i)
•  (2+1/√2)(1+i)
Solution
Q2. If x=2+2(2/3)+2(1/3), then the value of x3-6x2+6x is
•  3
•  2
•  1
•  -2
Solution

Q3. The principal argument of the complex number [〖(1+i)〗5 (1+√3i)2 ]/[-2i(-√3+i)] is
•  19Ï€/12
•  -7Ï€/12
•  -5Ï€/12
•  5Ï€/12
Solution

Q4. The range of a for which the equation x2+ax-4=0 has its smaller root in the interval (-1,2) is
•  (-∞,-3)
•  (0, 3)
•  (0,∞)
•  (-∞,-3)∪(0,∞)
Solution

Q5. If Î± and Î² are the roots of x2+px+q=0 and Î±4,Î²4 are the roots of x2-rx+s=0, then the equation x2-4qx+2q2-r=0 has always
•  One positive and one negative root
•  Two positive roots
•  Two negative roots
•  Cannot say anything
Solution

Q6. The number of solutions of the equation sin⁡〖(ex)〗=5x+5(-x) is
•  0
•  1
• 2
•  Infinitely many
Solution

Q7. If p(q-r)x2+q(r-p)x+r(p-q)=0 has equal roots, then 2/q=
•  1/p+1/r
•  p+r
•  p2+r2
•  1/p2 +1/r2
Solution

Q8. The roots of the equation t3+3at2+3bt+c=0 are z1,z2,z3 which represent the vertices of an equilateral triangle, then
•  a2=3b
•  b2=a
•  a2=b
•  b2=3a
Solution

Q9.  The integral values of m for which the roots of the equation mx2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer]
•  n2
•  n(n+2)
•  n(n+1)
•  None of these
Solution
Q10. Let z=1-t+i√(t2+t+2), where t is a real parameter. The locus of z in the Argand plane is
•  A hyperbola
•  An ellipse
•  A straight line
• None of these
Solution

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