Complex Numbers and Quadratic Equations (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 4 of 4

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Question number: 1

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2010

MCQ▾

Question

The roots of (x41)49+(x49)41+(x2009)2009=0 are –

Choices

Choice (4) Response

a.

Non-real except one positive real root

b.

Non-real except for three real roots of which exactly one is positive

c.

Non-real except three positive real roots

d.

All necessarily real

Question number: 2

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2011

MCQ▾

Question

Consider the cubic equation x3+ax2+bx+c=0 , where a, b, c are real numbers. Which of the following statements is correct?

Choices

Choice (4) Response

a.

If a22b>0, then the equation has all real and distinct roots

b.

If 4a327b2>, then the equation has real and distinct roots

c.

If a22b<0, then the equation has one real and two imaginary roots

d.

If a22b0, then the equation has all real roots

Question number: 3

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2012

MCQ▾

Question

Suppose a, b, c are real numbers, and each of the equations x2+2ax+b2=0 and x2+2bx+c2=0 has two distinct real roots. Then the equation x2+2cx+a2=0 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

Question number: 4

» Complex Numbers and Quadratic Equations » Algebra of Complex Numbers

Appeared in Year: 2015

MCQ▾

Question

If z is a complex number satisfying z3+z3 2 , then the maximum possible value of z+z1 is –

Choices

Choice (4) Response

a.

23

b.

22

c.

2

d.

1

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