Mathematics questions
18011 published questions with worked solutions.
- Let and the roots of the quadratic equation x^2 -x( +1)+ =0 (0< <45^ ), and < . Then _ n=0 ^ ( ^n+ (-1)^n ^n ) is equal to
- If be the ratio of the roots of the quadratic equation in x, 3m^2x^2+m(m-4)x+2=0, then the least value of m for which + 1 =1, is
- The number of integral values of m for which the quadratic expression, (1+2m)x^2-2(1+3m)x+4(1+m), x R, is always positive, is
- If and are the roots of the equation x^2-2x+2=0, then the least value of n for which ( )^n=1 is
- The sum of the solutions of the equation | x-2 |+ x ( x-4 )+2=0, (x>0) is equal to
- If three distinct numbers a,b,c are in G.P. and the equations ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root, then which one of...
- The number of integral values of m for which the equation (1+m^2 )x^2-2(1+3m)x+(1+8m)=0 has no real root is
- Let p,q R. If 2- 3 is a root of the quadratic equation, x^2+px+q=0, then
- If m is chosen in the quadratic equation (m^2+1 )x^2-3x+ (m^2+1 )^2=0 such that the sum of its roots is greatest, then the...
- If , and are three consecutive terms of a non-constant G.P. such that the equations x^2+2 x+ =0 and x^2+x-1=0 have a common root,...
- Let and be two real roots of the equation (k+1) ^2x- 2 x=(1-k), where k( -1) and are real numbers. If ^2( + )=50, then a value of...
- Let and be the roots of the quadratic equation x^2-x-1=0. If p_k=( )^k+( )^k, k 1, then which one of the following statements is...
- Let S be the set of all real roots of the equation, 3^x (3^x-1 )+2= |3^x-1 |+ |3^x-2 |. Then S
- Let a,b R, a 0 be such that the equation, ax^2-2bx+5=0 has a repeated root , which is also a root of the equation, x^2-2bx-10=0....
- Let f(x) be a quadratic polynomial such that f(-1)+f(2)=0. If one of the roots of f(x)=0 is 3, then its other root lies in
- If and are the roots of the equation x^2+px+2=0 and 1 and 1 are the roots of the equation 2x^2+2qx+1=0, then ( - 1 ) ( - 1 ) ( +...
- The set of all real values of for which the quadratic equations, ( ^2+1 )x^2-4 x+2=0 always have exactly one root in the interval...
- Let 0 be in R. If and are the roots of the equation, x^2-x+2 =0 and and are the roots of the equation, 3x^2-10x+27 =0, then is...
- The product of the roots of the equation 9x^2-18|x|+5=0, is
- If and are the roots of the equation, 7x^2-3x-2=0, then the value of 1- ^2 + 1- ^2 is equal to