IMO- Mathematics Olympiad Class 10: Questions 178 - 182 of 908

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Question number: 178

» Polynomials

MCQ▾

Question

A cubic polynomial with the sum of its zeroes, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively, is ________

Choices

Choice (4) Response

a.

x3−2x2−7x−14

b.

x3−2x2−7x+14

c.

x3+2x2+7x−14

d.

x3+2x2−7x−14

Question number: 179

» Polynomials

MCQ▾

Question

If αandβ are the zeroes of the polynomial f(x)=x2+px+q , then a polynomial having 1αand1β as its zeroes is ________

Choices

Choice (4) Response

a.

x2+qx+p

b.

px2+qx+1

c.

qx2+px+1

d.

x2−px+q

Question number: 180

» Pair of Linear Equations in Two Variables

MCQ▾

Question

Solve for x and y in the following question:

2x+2y+12x−y+59=0,9x+2y+62x−y+4=0

Choices

Choice (4) Response

a.

x=2,y=12

b.

x=12,y=2

c.

x=2,y=1

d.

x=1,y=2

Question number: 181

» Polynomials

MCQ▾

Question

If αandβ are the roots of the equation px2+qx+r=0 , then what is the quadratic equation whose roots are α1+αandβ1+β

Choices

Choice (4) Response

a.

px2−qx(x−1)+r(x−1)2=0

b.

px2+qx(x+1)+r(1+x)2=0

c.

px2−qx(1−x)+r(1−x)2=0

d.

px2+qx(1−x)+r(1−x)2=0

Question number: 182

» Pair of Linear Equations in Two Variables

MCQ▾

Question

The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 5, then numbers are ________

Choices

Choice (4) Response

a.

37, 73

b.

38, 83

c.

62, 26

d.

42, 24

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