Complex Numbers and Quadratic EquationsNature of Roots (KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math): Questions 1  3 of 3
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Question number: 1
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2010
Question
The roots of are –
Choices
Choice (4)  Response  

a.  Nonreal except one positive real root 

b.  Nonreal except for three real roots of which exactly one is positive 

c.  Nonreal except three positive real roots 

d.  All necessarily real 

Question number: 2
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2011
Question
Consider the cubic equation , where a, b, c are real numbers. Which of the following statements is correct?
Choices
Choice (4)  Response  

a.  If then the equation has all real and distinct roots 

b.  If then the equation has real and distinct roots 

c.  If then the equation has one real and two imaginary roots 

d.  If then the equation has all real roots 

Question number: 3
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2012
Question
Suppose a, b, c are real numbers, and each of the equations and has two distinct real roots. Then the equation has –
Choices
Choice (4)  Response  

a.  Two equal roots 

b.  No real roots 

c.  One positive and one negative root 

d.  Two distinct positive real roots 
