### Eamcet - Maths - Theory Of Equations Test

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If m,n,k are rational and m=k+(n/k),then the roots of x2+mx+n=0 are

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

If α,β are the roots of 3x2-5x+7=0 then α3+β3=

The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is

The equation ax2+bx+c=0 (a,bR) and x3-2x2+2x-1=0 have two roots common.Then a+b must equal to

If 1,-1,3 are the roots of x3+Ax2+Bx+C=0 then the ascending order of A,B,C is

The equations whose roots are squares of the roots of x4+x3+2x2+x+1=0 is

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=

If α,β,γ are the roots of 4x3-6x2+7x+3=0 then αβ+βγ+αγ=

If α,β,γ are the roots of x3-px2+qx-r=0,then Σα2(β+γ)=

If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=

The equation whose roots are 2√3-5 and -2√3-5 is

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

The multiple roots of x4-2x3+11x2-12x+36=0 are

If two roots of x3-4x2+x+6=0 are in the ratio 2:3 then the roots are

If the roots of ax3+bx2+cx+d=0 are in G.P then the roots of dx3-cx2+bx-a=0 are in

The equation of the lowest degree with rational coefficients having a root √2+√3+i is

If α,β,γ are the roots of x3+qx+r=0 then the equation whose roots βγ+1/α,γα+1/β,αβ+1/γ is

The equations whose roots are exceed by 2 than those of x4+x3-10x2+4x+24=0 is

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

If x4+4x3-2x2-12x+9=0 has a pair of equal roots then the roots are

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ1/α β=

If both the roots of the equation x2-6ax+2-2a+9a2=0 exceed 3,then

If ax2+2bx+c=0,a1x2+2b1x+c1=0 have a common root,then the roots of the equation (b2-ac)x2+(2bb1-ac1-a1c)x+(b12-a1c1)=0 are

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

If α,β,γ are the roots of the equation x3-px2+qx-r=0,then α3β3γ3=

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

If 12x2-10xy+2y2+11x-5y+k is resolvable into two linear factors then k=

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

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