Practice questions
88551 published questions with worked solutions.
- If the absolute value of the difference of the roots of the equation x^2+ax+1=0 exceeds 3a , then
- If p and q are roots of the quadratic equation x^2+mx+m^2+a=0, then the value of p^2+q^2+pq is
- If the equations k (6x^2+3 )+rx+2x^2-1=0 and 6k (2x^2+1 )+px+4x^2-2=0 have both roots common, then the value of (2r-p) is
- The value of k for which the equation 3x^2+2 (k^2+1 )x+k^2-3k+2=0 has roots of opposite signs, lies in the interval
- If x^2-2ra_rx+r=0; r=1,2,3 are three quadratic equations of which each pair has exactly one root common, then the number of...
- If x R, the least value of the expression x^2-6x+5 x^2+2x+1 , is
- If x,a,b,c are real and (x-a+b)^2+(x-b+c)^2=0, then a,b,c are in
- The equation 2 ^2 ( x2 ) ^2x=x^2+ 1 x^2 , 0 x 2 hasNot in JEE Main syllabus
- The number of quadratic equations which are unchanged by squaring their roots is
- If x^2-bx ax-c = -1 +1 has roots equal in magnitude and opposite in sign then the value of is
- The roots , and of an equation x^3-3ax^2+3bx-c=0 are in H.P. Then,
- If the sum of the squares of the roots of the equation x^2-(a-2)x-(a+1)=0 is least, then the value of a is
- The value of m for which the equation x^3-mx^2+3x-2=0 has two roots equal in magnitude but opposite in sign, is
- If the roots of x^3-12x^2+39x-28=0 are in A.P., then their common difference is
- The value of k for which the equation (k-2)x^2+8x+k+4=0 has both roots real, distinct and negative, is
- If the sum of the squares of the roots of the equation x^2-( -2)x-(1+ )=0 is least, then =
- The roots of the equation |x^2-x-6 |=x+2 are
- The value of k' for which one of the roots of x^2-x+3k=0, is double of one of the roots of x^2-x+k=0 is
- The quadratic equations x^2+ (a^2-2 )x-2a^2=0 and x^2-3x+2=0 have
- If A= x:f(x)=0 and B= x:g(x)=0 , then A B will be the set of roots of the equation