Polynomials (IMO- Mathematics Olympiad Class 10): Questions 51 - 55 of 81

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Question number: 51

» 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.

x2px+q

Question number: 52

» 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.

px2qx(x1)+r(x1)2=0

b.

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

c.

px2qx(1x)+r(1x)2=0

d.

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

Question number: 53

» Polynomials

MCQ▾

Question

If αandβ are the roots of the equation 2x23x5=0 , then the equation whose roots are α+1β and β+1α is ________

Choices

Choice (4) Response

a.

x2x+11=0

b.

x2x11=0

c.

x2x11=0

d.

x2+x+11=0

Question number: 54

» Polynomials

MCQ▾

Question

For x2+2x+5 to be a factor of x4+px2+q , the value of p and q should respectively be ________

Choices

Choice (4) Response

a.

2, 5

b.

5, 2

c.

6, 25

d.

5, 25

Question number: 55

» Polynomials

MCQ▾

Question

When 6x226x+12 is divided by x4 , the quotient and remainder is ________

Choices

Choice (4) Response

a.

x+2,4

b.

6x2,4

c.

6x+2,2

d.

x2,4

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