Mathematics questions
18011 published questions with worked solutions.
- 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...
- cosec 18^ is a root of the equation
- The number of pairs (a,b) of real numbers, such that whenever is a root of the equation x^2+ax+b=0, ^2-2 is also a root of this...
- If and are the roots of the quadratic equation, x^2+x -2 =0, (0, 2 ), then ^ 12 + ^ 12 ( ^ -12 + ^ -12 ) ( - )^ 24 is equal to
- If , are the roots of the equation x^2- (5+3^ _35 -5^ _53 )x+3 (3^ _35 -5^ _53 -1 )=0, then the equation, whose roots are + 1 and...
- Let , be the roots of the equation x^2- 2x+ 6=0 and 1 ^2 +1, 1 ^2 +1 be the roots of the equation x^2+ax+b=0. Then the roots of...
- Let f(x)=ax^2+bx+c be such that f(1)=3, f(-2)= and f(3)=4. If f(0)+f(1)+f(-2)+f(3)=14, then is equal to
- If the sum of the squares of the reciprocals of the roots and of the equation 3x^2+ x-1=0 is 15, then 6 ( ^3+ ^3 )^2 is equal to
- The sum of all the real roots of the equation (e^ 2x -4 ) (6e^ 2x -5e^x+1 )=0 is
- Let a,b R be such that the equation ax^2-2bx+15=0 has a repeated root . If and are the roots of the equation x^2-2bx+21=0, then...
- Let f(x) be a quadratic polynomial such that f(-2)+f(3)=0. If one of the roots of f(x)=0 is -1, then the sum of the roots of...
- The minimum value of the sum of the squares of the roots of x^2+(3-a)x+1=2a is