Eamcet - Maths - Theory Of Equations Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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The equations whose roots are those of equation x4-3x3+5x2-2=0 with contrary signs

  

  

  

  

The roots of x4-12x3+34x2-12x+1=0 are

  

  

  

  

If α and β are different values of x satisfying a cos x+b sin x=c then tan (α+β/2) =

  

  

  

  

If one root of x3+3x2+5x+k=0 may be the sum of the other two roots then k=

  

  

  

  

If x2-3x+2 is a factor of x4-px2+q=0,then(p,q)=

  

  

  

  

If α,β,γ are the roots of x3-7x+6=0 then the equation whose roots are (α–β)2,(β–γ)2,(γ–α)2 is

  

  

  

  

If 1,-2,3 are roots of x3-2x2+ax+6=0 then a=

  

  

  

  

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

  

  

  

  

The roots of 6x6-25x5+31x4-31x2+25x-6=0 are

  

  

  

  

If 2,3 are the roots of the equation 2x3+px2-13x+q=0,then (p,q)=

  

  

  

  

If f(x) is a polynomial of degree n with rational coefficients and 1+2i, 2-√3 and 5 are three roots of       f(x) = 0, then the least value of n is :

  

  

  

  

The value of a for which each one of the roots of x2-4ax+2a2-3a+5=0 is greater tan 2,are

  

  

  

  

The condition that a root of ax2+bx+c=0 may be the reciprocal of a root of a1x2+b1x+c1=0 is

  

  

  

  

If cos 2x = (√2 + 1)(cos x - 1/√2) , cos x ≠ 1/2 then x belongs to

  

  

  

  

The sum of the fourth powers of the roots of the equation x4-x3-7x2+x+6=0 is

  

  

  

  

If the roots of the equation x2+a2=8x+6a are real,then a lies between

  

  

  

  

If α,β are the roots of x2-p(x+1)+c=0 then (1+α)(1+β)=

  

  

  

  

The value of b so that x4-3x3+5 x2-33x+b is divisible by x2-5x+6 is

  

  

  

  

If x2+px+q=0 and x2+qx+p=0 have a common root,then their other roots are the roots of

  

  

  

  

If α,β,γ are the roots of x3+2x2-3x-1=0,then the value of α-4+β-4+γ-4 is

  

  

  

  

If -1+I is a root of x4+4x3+5x2+2x+k=0 then k=

  

  

  

  

If two roots of 2x3-x2-22x-24=0 are in the ratio 3:4 then the roots are

  

  

  

  

If x4-5x3+9x2-7x+2=0 has a multiple root of order 3 then the roots are

  

  

  

  

The roots of the equation (b-c)x2+(c-a)x+(a-b)=0 are

  

  

  

  

The equations whose roots are exceed by 1 than those of x3-5x2+6x-3=0 is

  

  

  

  

If α,β,γ are the roots of x3-2x2+3x+5=0 then the equation whose roots are β2γ2,γ2α2,α2β2 is

  

  

  

  

If α+β+γ=1,α2+β2+γ2=2 and α3+β3+γ3=3,then α5+β5+γ5=

  

  

  

  

The roots of x5-5x4+9x3-9x2+5x-1=0 are

  

  

  

  

If α,β and γ are roots of x3+ax2+bx+c=0 then(α2+1)(β2+1)(γ2+1)

  

  

  

  

The quotient we get when we divide x4-8x3+25 x2-46x+40 with -6x+8 is

  

  

  

  

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