Complex Numbers and Quadratic Equations (KVPY StreamSA (Class 11) Math): Questions 7  11 of 27
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Question number: 7
» Complex Numbers and Quadratic Equations » Quadratic Equations in Real and Complex Number System
Appeared in Year: 2013
Question
In an acuteangled triangle ABC, the altitudes from A, B, C when extended intersect the circle again at points A_{1}, B_{1}, C_{1}, respectively. If ∠ABC = 45° then ∠A_{1}B_{1}C_{1} equals.
Choices
Choice (4)  Response  

a.  135° 

b.  45° 

c.  60° 

d.  90° 

Question number: 8
» Complex Numbers and Quadratic Equations » Relation Between Roots and Coefficients
Appeared in Year: 2012
Question
Let be a quadratic polynomial with and . Then the coefficient of in is
Choices
Choice (4)  Response  

a.  1 

b.  4 

c.  2 

d.  3 

Question number: 9
» Complex Numbers and Quadratic Equations » Complex Numbers as Ordered Pairs of Reals
Appeared in Year: 2012
Question
How many ordered pairs of (m, n) integers satisfy ?
Choices
Choice (4)  Response  

a.  30 

b.  10 

c.  15 

d.  12 

Question number: 10
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2013
Question
Let a, b be nonzero real numbers. Which of the following statements about the quadratic equation.
Is necessarily true?
(I) It has at least one negative root
(III) Both roots are negative
(II) Both its roots are real.
(IV) It has at least one positive root.
Select the correct option,
Choices
Choice (4)  Response  

a.  (III) and (IV) are correct 

b.  (I) and (II) are correct 

c.  (I), (II) and (III) are correct 

d.  (I) and (III) are correct 

Question number: 11
» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots
Appeared in Year: 2014
Question
Let and , where a and b are positive integers. Suppose and . If the coefficient of the highest degree term of k (x) is 1, the sum of the roots of is
Choices
Choice (4)  Response  

a.  6 

b.  5 

c.  4 

d.  7 
