IMO- Mathematics Olympiad Class 10: Questions 91 - 95 of 889

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Question number: 91

» 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: 92

» 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: 93

» 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

Question number: 94

» Polynomials

MCQ▾

Question

If αandβ are the roots of the equation x2px+q=0 , then the quadratic equation whose roots are αβ and βα is ________

Choices

Choice (4) Response

a.

px2+(2p2q2)x+q=0

b.

qx2+(2qp2)x+q=0

c.

qx2+(p22q)x+q=0

d.

qx2px+1=0

Question number: 95

» Polynomials

MCQ▾

Question

If αandβ are the roots of the equation 2y23y+1=0 , then the equation whose roots are α2β+3 and β2α+3 is ________

Choices

Choice (4) Response

a.

40x2+14x+1=0

b.

40x214x+1=0

c.

40x2+14x+1=0

d.

40x214x1=0

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