Practice questions
88551 published questions with worked solutions.
- If a 0, then one of the roots of x^2-2a|x-a|-3a^2=0 is
- If and are roots of the quadratic equation x^2+4x+3=0, then the equation whose roots are 2 + and +2 is
- If two equations x^2+a^2=1-2ax and x^2+b^2=1-2bx have only one common root, then
- If both the roots of the quadratic equation x^2-2kx+k^2+k-5=0 are less than 5, then k lies in the interval
- If , , are the roots of x^3+4x+1=0, then the equation whose roots are ^2 + , ^2 + , ^2 + is
- The quadratic equations x^2-6x+a=0 and x^2-cx+6=0 have one root in common. The other roots of the first and second equations are...
- The quadratic equation whose roots are three times the roots of 3ax^2+3bx+c=0 is
- Let a,b,c be real, if ax^2+bx+c=0 has two real roots and , where <-2 and >2, then
- For a b, if the equation x^2+ax+b=0 and x^2+bx+a=0 have a common root, then the value of a+b equals
- The equation whose roots are reciprocal of the roots of the equation ax^2+bx+c=0 is
- If a,b,c are in GP, then the equation ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root, if da, eb, fc are in
- All the values of m for which both roots of the equation x^2-2mx+m^2-1=0 are greater than -2 but less than 4 lie in the interval
- Let a,b,c be real. If ax^2+bx+c=0 has two real roots and , where <-1 and >1, then 1+ ca+ | ba | is
- If ax^2+bx+c=0 and 2x^2+3x+4=0 have a common root where a,b,c N (set of natural numbers), the least value of a+b+c is
- If x is real, then x^2-2x+4 x^2+2x+4 takes values in the interval
- If x is real, the expression x^2+34x-71 x^2+2x-7 takes all values except those which lie in the interval (a,b) where
- If (x^2-3x+2 ) is a factor of x^4-px^2+q=0, then the values of p and q are
- If x is real, then the minimum value of x^2-x+1 x^2+x+1 , is
- If the roots of the equation bx^2+cx+a=0 be imaginary, then for all real values of x, the expression 3b^2x^2+6bcx+2c^2 is
- If x is real, then the value of x+2 2x^2+3x+6 lies in