Polynomials (IMO- Mathematics Olympiad Class 10): Questions 1 - 7 of 81

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Question number: 1

» Polynomials

MCQ▾

Question

If the zero of the quadratic polynomial x22x+k is 3, then the value of k is ________

Choices

Choice (4) Response

a.

-8

b.

-3

c.

6

d.

-1

Question number: 2

» Polynomials

MCQ▾

Question

If α,β,γ are the roots of the cubic 4x3+3x22x5 , the value of 1α+1β+1γ is ________

Choices

Choice (4) Response

a.

25

b.

52

c.

25

d.

52

Question number: 3

» Polynomials

MCQ▾

Question

If α,β are the roots of x2+3x+7=0 then a2+b2 is ________

Choices

Choice (4) Response

a.

-10

b.

-5

c.

-15

d.

-20

Question number: 4

» Polynomials

MCQ▾

Question

If one zero of the polynomial (k2+25)x2+30x+10k is a reciprocal of the other, then k is equal to ________

Choices

Choice (4) Response

a.

2

b.

9

c.

7

d.

5

Question number: 5

» Polynomials

MCQ▾

Question

If αandβ are the roots of the equation 2x25x7=0 , then the equation whose roots are 2α+3β and 3α+2β is ________

Choices

Choice (4) Response

a.

2x225x+68=0

b.

x2+25x+68=0

c.

2x2+25x68=0

d.

2x225x68=0

Question number: 6

» Polynomials

MCQ▾

Question

The difference of roots of the quadratic equation 6p25p+1=0 is ________

Choices

Choice (4) Response

a.

16

b.

56

c.

16

d.

56

Question number: 7

» Polynomials

MCQ▾

Question

The sum of the reciprocals of the roots of the equation 5x2+10x15=0 is ________

Choices

Choice (4) Response

a.

32

b.

23

c.

23

d.

32

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