Complex Numbers and Quadratic Equations-Quiz-19

Complex Number and Quadratic Equations Quiz-19

Dear Readers,

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

•  19π/12
•  -7π/12
•  -5π/12
•  5π/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 α and β are the roots of x²+px+q=0 and α⁴,β⁴ 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⁡〖(e^x)〗=5^x+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