Practice questions
88551 published questions with worked solutions.
- The common roots of the equations x^3+2x^2+2x+1=0 and 1+x^ 2002 +x^ 2003 =0 are (where is a complex cube root of unity)
- If a,b,c are real numbers in G.P. such that a and c are positive, then the roots of the equation ax^2+bx+c=0
- The sum of non-real roots of the equation (x^2+x-2 ) (x^2+x-3 )=12, is
- The number of non-zero solutions of the equation x^2-5x- ( Sgn (x) )6=0, is
- The number of positive integral roots of x^4+x^3-4x^2+x+1=0 is
- If both the roots of the equation ax^2+bx+c=0 are zero, then
- If x^2+ax+10=0 and x^2+bx-10=0 have a common root, then a^2-b^2 is equal to
- The number of real roots of the equation (x+3)^4+(x+5)^4=16, is
- If (1+k) ^2x-4 x-1+k=0 has real roots x_1 and x_2, then
- If the roots of the equation x^2+a^2=8x+6a are real, then a belongs to the interval
- The equations ax^2+bx+a=0 and x^3-2x^2+2x-1=0 have 2 roots in common. Then a+b must be equal to
- If z any complex number satisfying |z-3-2i| 2, then the minimum value of |2z-6+5i| is
- For an integer k, let _k= [ k 7 ]+i [ k 7 ], where i= -1 . The value of the expression _ k=1 ^ 12 | _ k+1 - _k| _ k=1 ^3| _ 4k-1...
- Let =e^ i /3 and a,b,c,x,y,z be non-zero complex numbers such that (relations not printed in the source). Then, the value of...
- The smallest value of k, for which both the roots of the equation x^2-8kx+16 (k^2-k+1 )=0 are real, distinct and have values at...
- For a positive integer n, if the quadratic equation x(x+1)+(x+1)(x+2)+ +(x+n-1)(x+n)=10n has two consecutive integral solutions,...
- Let - 6< <- 12 . Suppose _1 and _1 are the roots of the equation x^2-2x +1=0, and _2 and _2 are the roots of the equation x^2+2x...
- Let and be the roots of equation x^2-6x-2=0. If a_n= ^n- ^n for n 1, then the value of a_ 10 -2a_8 2a_9 is
- The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has
- Let and be the roots of equation px^2+qx+r=0, p 0. If p,q and r are in A.P. and 1 + 1 =4, then the value of | - | is