Practice questions
88551 published questions with worked solutions.
- 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
- Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0)=p, p 0, and f(1)= 13. If the equations f(x)=0 and f...
- Let R and let the equation E be |x|^2-2|x|+| -3|=0. Then the largest element in the set S= x+ :x is an integer solution of E is
- Let m and n be the numbers of real roots of the quadratic equations x^2-12x+[x]+31=0 and x^2-5|x+2|-4=0 respectively, where [x]...
- The number of elements in the set n Z: |n^2-10n+19 |<6 is
- Let S= z C- i,2i : z^2+8iz-15 z^2-3iz-2 R . If - 13 11 i S, R- 0 , then 242 ^2 is equal to
- The least positive value of a for which the equation, (the equation is not legible in the source), has real roots is
- If x=-1,-4 are roots of the equation x=-1 and C-3:x - ,-2) for each positive integer -x^2+5x+16=0, then the value of x^2-5x-16=0...
- The sum of all integral values of k (k 0) for which the equation 2 x-1 - 1 x-2 = 2k in x has no real roots, is
- If for some p,q,r R, not all have same sign, one of the roots of the equation (p^2+q^2 )x^2-2q(p+r)x+q^2+r^2=0 is also a root of...