Practice questions
88551 published questions with worked solutions.
- 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
- If and be two roots of the equation x^2-64x+256=0. Then the value of ( ^3 ^5 )^ 1/8 + ( ^3 ^5 )^ 1/8 is
- If and are the roots of the equation 2x(2x+1)=1, then is equal to
- The integer 'k', for which the inequality x^2-2(3k-1)x+8k^2-7>0 is valid for every x in R, is
- Let and be the roots of x^2-6x-2=0. If a_n= ^n- ^n for n 1, then the value of a_ 10 -2a_8 3a_9 is
- The number of real roots of the equation e^ 6x -e^ 4x -2e^ 3x -12e^ 2x +e^x+1=0 is
- The number of real solutions of the equation, x^2-|x|-12=0 is
- Let , be two roots of the equation x^2+(20)^ 1/4 x+(5)^ 1/2 =0. Then ^8+ ^8 is equal to
- Let = _ x R 8^ 2 3x 4^ 4 3x and = _ x R 8^ 2 3x 4^ 4 3x . If 8x^2+bx+c=0 is a quadratic equation whose roots are ^ 15 and ^ 15 ,...
- The set of all values of k>-1, for which the equation (3x^2+4x+3 )^2-(k+1) (3x^2+4x+3 ) (3x^2+4x+2 )+k (3x^2+4x+2 )^2=0 has real...