IMO- Mathematics Olympiad Class 10: Questions 232 - 237 of 889

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Question number: 232

» Polynomials

MCQ▾

Question

The roots of the quadratic equation 8x22kx+20=0 are in the ratio 5:2 , then k equals ________

Choices

Choice (4) Response

a.

10

b.

11

c.

14

d.

13

Question number: 233

» Polynomials

MCQ▾

Question

If αandβ are the zeroes of the quadratic polynomial f(x)=x27x+5 , then the value of α3+β3 is ________

Choices

Choice (4) Response

a.

260

b.

238

c.

250

d.

228

Question number: 234

» Pair of Linear Equations in Two Variables

MCQ▾

Question

The sum of two numbers is 7 and the sum of their squares is 29. The numbers are ________

Choices

Choice (4) Response

a.

9 and 6

b.

2 and 5

c.

1 and 2

d.

8 and 5

Question number: 235

» 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 6, 17, 12 respectively, is ________

Choices

Choice (4) Response

a.

x36x2+17x12

b.

x36x2+17x+12

c.

x3617x12

d.

x3+6x2+17x12

Question number: 236

» Polynomials

MCQ▾

Question

If one zero of the cubic polynomial p(x)=x36x2+11x6 is 1, then other two zeroes are ________

Choices

Choice (4) Response

a.

2, -3

b.

-2, -3

c.

-2, 3

d.

2, 3

Question number: 237

» Polynomials

MCQ▾

Question

If α,β are the roots of ax22bxc=0 then a3b3+a2b3+a3b2 is ________

Choices

Choice (4) Response

a.

(c+2b)a3

b.

c2(c+2b)a3

c.

c2(c+2b)a2

d.

c2(2b)a3

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