Complex Numbers and Quadratic Equations-Formation of Quadratic Equations With Given Roots (KVPY Stream-SA (Class 11) Math): Questions 1 - 5 of 7

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Question number: 1

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

Appeared in Year: 2011

MCQ▾

Question

If x+1x=a,x2+1x3=b , then x3+1x2 is,

Choices

Choice (4) Response

a.

a 3 + a 2 + 3 a - 16 - b

b.

a3a23a+4b

c.

a 3 - a 2 + 3 a - 6 - b

d.

a3+a23a2b

Question number: 2

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

Appeared in Year: 2013

MCQ▾

Question

Let x, y, z be non-zero real numbers such that xy+yz+zx=7 and yx+zy+xz=9 , then x3y3+y3z3+z3x33 is equal to

Choices

Choice (4) Response

a.

153

b.

154

c.

152

d.

155

Question number: 3

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

MCQ▾

Question

Let p, q, r be non-zero real numbers such that pq+qr+rp=10 and qp+rq+pr=12 , then p3q3+q3r3+r3p33 is equal to,

Choices

Choice (4) Response

a.

553

b.

550

c.

640

d.

654

Question number: 4

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

Appeared in Year: 2014

MCQ▾

Question

Let p(x)=x25x+a and q(x)=x23x+b , where a and b are positive integers. Suppose hcf(p(x),q(x))=x1 and k(x)=lcm(p(x),q(x)) . If the coefficient of the highest degree term of k (x) is 1, the sum of the roots of (x1)+k(x) is

Choices

Choice (4) Response

a.

6

b.

5

c.

4

d.

7

Question number: 5

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

MCQ▾

Question

If α, β are the roots of ax2+bx+c=0, then that equation whose roots are 1α+β,1α+1β is –

Choices

Choice (4) Response

a.

bcx2+(b2+ac)x+ab=0

b.

acx2+(a2+bc)x+bx=0

c.

abx2+(c2+ab)x+ca=0

d.

None of the above

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