Polynomials (IMO- Mathematics Olympiad Class 10): Questions 20 - 25 of 80

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Question number: 20

» Polynomials

MCQ▾

Question

If α,β be the zeroes of the quadratic polynomial 2x2+5x+1 , then the value of α+β+αβ =________

Choices

Choice (4) Response

a.

4

b.

1

c.

-2

d.

-1

Question number: 21

» Polynomials

MCQ▾

Question

If a and b are the roots of the equation x2px+q=0 , then the equation if the roots are (ab+a+b)and(abab) ?

Choices

Choice (4) Response

a.

pqx22(p+q)x+q2=0

b.

x22px+(p2q2)=0

c.

x22qx+(q2p2)=0

d.

x22px+(q2p2)=0

Question number: 22

» Polynomials

MCQ▾

Question

If a and b are the roots of the quadratic equation x2+px+12=0 with the condition ab=1 , then the value of ‘p’ is ________

Choices

Choice (4) Response

a.

7 or -7

b.

7

c.

1

d.

-7

Question number: 23

» Polynomials

MCQ▾

Question

When 4x418x3+42x252x+24 is divided by 4x6 , the quotient and remainder is ________

Choices

Choice (4) Response

a.

x33x2+6x4,0

b.

x3+3x2+6x+4,0

c.

x33x26x4,3

d.

x3+3x2+6x4,3

Question number: 24

» Polynomials

MCQ▾

Question

If the sum of the squares of zeroes of the polynomial 4x2+12x+k is 616 , find the value of k

Choices

Choice (4) Response

a.

754

b.

475

c.

1834

d.

Both a. and c. are correct

Question number: 25

» Polynomials

MCQ▾

Question

If α,β be the zeroes of the quadratic polynomial 2x26x+8 , then the value of αβα2+β2 =________

Choices

Choice (4) Response

a.

-5

b.

-4

c.

5

d.

4

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